As I explained in a previous and related post, the expression "Urim and Thummim" is never used in the Book of Mormon. Instead, the term was likely adopted by the Prophet during or after his translation of the Old Testament once he became familiar with the Old Testament revelatory device known to the ancients as the Urim & Thummim. In fact, the reference to the “Urim and Thummim” found in D&C 10:1 was added in the 1835 edition of the D&C. Prior to that the word “interpreters” was used, which is consistent with Book of Mormon terminology referring to the Nephite interpreters. While it isn’t technically correct, it eventually became common for members of the Church to call the Nephite interpreters the Urim & Thummim.
So, who do we know of that had a Urim & Thummim, and do any of them relate to each other?
1) “And I, Abraham, had the Urim and Thummim, which the Lord my God had given unto me, in Ur of the Chaldees” (Abr. 3:1). A Urim & Thummim was given to Abraham while he resided in Ur, and he was taught astronomy through it (Abr. 3:1-4). “And the Lord said unto me, by the Urim and Thummim, that Kolob was after the manner of the Lord” (Abr. 3:4). It’s interesting to note that, although Abraham used the Urim & Thummim to receive revelation from the Lord, he also “talked with the Lord, face to face, as one man talketh with another” (Abr. 3:11). The scriptures are silent as to what happened to Abraham’s Urim & Thummim.
2) Aaron and the priests of Israel also had a Urim & Thummim that was passed down from generation to generation (see Ex. 28:30; Lev. 8:8; Deut. 33:8; 1 Sam. 28:6; and Neh. 7:65). Although not stated in scripture, it is not improbable nor would it be surprising if this were the same Urim & Thummim that Abraham had. Nevertheless, the scriptures do not indicate how Aaron received the Urim & Thummim.
Though no clear explanation has been preserved for us scripturally, the device used by Aaron likely consisted of ocular objects belonging to the ephod or vestment of the high priest. The Urim & Thummim were carried in the breastplate of judgment, which bore the names of the 12 tribes of Israel on 12 precious stones so as to be on the high priest’s heart when he went before the Lord (see Exodus 28:15-30). Through apostasy, the use of the Urim & Thummim was lost to Israel. Thus, when the Jews returned from their Babylonian captivity and they were faced with a tough question, it was agreed to postpone their answer until there should rise up “a priest with Urim and with Thummim” (Ezra 2:63).
3) The brother of Jared received a Urim & Thummim, or "two stones" adapted for interpretation. Atop Mount Shelem, the brother of Jared was privileged to see and record some of the most sacred things ever revealed unto a mortal, including single-handedly parting the veil through his own faithfulness in order to behold the Lord Jesus Christ before he took upon himself a mortal tabernacle. Indeed, “there never were greater things made manifest than those which were made manifest unto the brother of Jared” (Ether 4:4). Because of the sacred nature of his visions, the brother of Jared was commanded to record what he saw “in a language that they cannot be read,” “[f]or behold, the language which ye shall write I have confounded” (Ether 3:22, 24).
In order to provide an interpretation for future righteous generations privileged to read his record, the Lord provided the brother of Jared with “two stones” (e.g., Nephite interpreters) that were to be sealed up with his record (Ether 3:23, 28).
4) King Mosiah I, the father of King Benjamin, translated engravings written on a large Jaredite stone “by the gift and power of God” (Omni 1:20). As understood by LDS, translating “by the gift and power of God” is synonymous with using a Urim & Thummim, or the Nephite interpreters as it were in this case (see D&C 135:3; Introduction to the Book of Mormon). The Nephite interpreters were described as “two stones which were fastened into the two rims of a bow” (Mosiah 28:13). How King Mosiah I received the stones is not readily apparent, neither is it known who put them into the rims of a bow. The interpreters eventually passed from Mosiah I to his grandson King Mosiah II, who translated the Jaredite record found by Limhi’s people (see Mosiah 8:13-14; Mosiah 28:11-15).
I feel it is plausible that the Nephite interpreters used by Kings Mosiah I & II were likely the same interpreters (i.e., two stones) used by the brother of Jared. Mormon explained that the interpreters had “been kept and preserved by the hand of the Lord” to translate the brother of Jared’s writings (see Mosiah 28:15), and Moroni indicated that Mosiah II received (and likely translated/read) the brother of Jared’s account (see Ether 4:1). While the scriptures do not specifically state this, it may be reasonable to assume that whoever brought Mosiah I the Jaredite stone to translate also delivered to him the brother of Jared’s interpreters.
On the other hand, if that were the case, why didn’t these individuals also grab and deliver up the brother of Jared’s record to Mosiah I, which was specifically sealed up with the stones? Why did his record not come forward until Limhi’s people found it? Unfortunately, there is no explanation given in the scriptures. Regardless, the scriptures are clear that Mosiah II had interpreters in his possession when Limhi’s people presented him with the Jaredite record. Whether his interpreters were those had by the brother of Jared, we cannot be certain, but a reasonable argument can be made to that effect.
5) Alma received the Nephite interpreters from King Mosiah II (Mosiah 28:20). The interpreters were then passed from one record keeper to the next until Mormon gave them to Moroni who was commanded to seal up the interpreters (specifically, the brother of Jared’s interpreters) in the Hill Cumorah (Ether 4:5). Since there is no record of Mormon or Moroni receiving any other interpreters besides those coming through Mosiah I & II, and we know it was the brother of Jared’s interpreters that were sealed within the Hill Cumorah (see point 6 below), I again feel it plausible that Kings Mosiah I & II used the stones had by the brother of Jared.
On a side note, we also know that Moroni was privileged to read the brother of Jared’s record (see Ether 4:4), which would have required him to translate it using the two stones. Also, there is a good possibility that the righteous generations spoken of in 4 Nephi were privileged to translate and read the record (see Ether 4:1-2).
6) The Prophet Joseph Smith unearthed and used the brother of Jared’s Urim & Thummim to translate the Book of Mormon (D&C 17:1). The Prophet described the Urim & Thummim as “two transparent stones set in the rim of a bow fastened to a breastplate” (History of the Church, 4:537). Lucy Mack Smith was able to inspect the Urim & Thummim the morning after Joseph had obtained them from the Hill Cumorah. She stated that she “took the article in [her] hands and, examining it with no covering but a silk handkerchief, found that it consisted of two smooth three-cornered diamonds set in glass, and the glasses were set in silver bows connected with each other in much the same way that old-fashioned spectacles are made” (History of Joseph Smith, 1996, p.139).
7) The planet on which God resides is also described as being “a great Urim and Thummim,” and the earth itself in its “sanctified and immortal state,” will also be a Urim & Thummim (D&C 130:8-9).
Finally, the white stone given to each inhabitant of celestial glory will be a Urim & Thummim “whereby things pertaining to a higher order of kingdoms will be made known” (D&C 130:10; see also Revelation 2:17).
Feel free to comment if I missed something.