“... it was not the first time Moses and the LORD Jesus Christ had met to talk.”
There’s an interesting theory that the “Angel of the Lord” who appears at various times throughout the OT was the pre-incarnation Christ. The main evidence is that while other angels take pains to warn men not to offer them veneration, this angel alone accepted it, which would make sense if he really was the Son.
Not having access to the Vatican and other private collections that might shed some light, all I have is the Holy Bible and the Holy Spirit with me to point out what pertains to me and/or what I am to be doing.
That said, I guess that the Angel of the Lord was Gabriel or Michael or another. But I believe Moses encountered THE LORD Himself on Sinai, and not an Emissary of The Lord.
There is a theological term for that, "Theophany":
Following are a number of what may be considered classic theophanies. The Lord appears to Abraham on his arrival in the land, wherein God promised the land to Abraham and his descendants ( Gen 12:7-9 ); God reaffirmed his promises of land and progeny when Abraham was ninety-nine years old ( Gen 17:1 ), and on the Plains of Mamre on his way to destroy Sodom ( Gen 18:1 ).
God appeared to Jacob in his dream at Bethel ( Gen 28:11-19 ). It is also clear that in the events at the Jabbok ford, Jacob somehow received a revelation through an encounter with God, although neither a strict reading of the text ( Gen 32:22-32 ) nor its later interpretation by Hosea ( 12:3-4 ) demand a theophany.
God appeared to Moses alone on the mountain ( Exod 19:20 ; 33:18-34:8 ). God also appeared to Moses, with Aaron and his sons and the seventy elders ( Exod 24:9-11 ) and in the transfer of leadership to Joshua ( Deut 31:15 ).
While he suffered, Job had complained that he sought an audience with God ( 31:35 ). At the conclusion of the book the Lord appears in a thunderstorm to deliver two discourses, designed to grant Job's request for a hearing and arguably to supply at least one of the meanings for Job's affliction: God is sovereign.
In a looser sense, God's promise of the land to Abraham ( Gen 15 ), as well as his commission that Abraham sacrifice Isaac ( Gen 22 ), could be considered theophanies. Frequently the term, "glory of the Lord, " reflects a theophany, as in Exodus 24:16-18; the "pillar of cloud" has a similar function in Exodus 33:9. The Spirit of God or the Spirit of the Lord must be considered theophanous, particularly when it comes upon men, transforming them ( 1 Sam 10:6 ) and equipping them for divine service ( 1 Sam 16:13 ). The Lord appears to people in visions ( Gen 15:1 ; 46:2 ; Job 33:15 ; Psalm 89:19 ; Dan 2:19 ; Acts 9:10 ; 18:9 ) and in dreams ( Gen 20:3 ; 31:24 ; 1 Kings 3:5 ; Matt 2:13 ) to reveal his plans for them or to unveil mysteries for the future.
The Lord appears in theophanies both to bless and to judge. A frequent introduction for theophanies may be seen in the words, "The Lord came down." Examples may be found in Genesis 11:5, Exodus 34:5, Number 11:25, and Numbers 12:5. Although the most common verb for the manifestation of the glory of the Lord is "appeared" ( Lev 9:23 ; Num 14:10 ; Numbers 16:19 Numbers 16:42 ; 20:6 ), God's glory also "settled" on Mount Sinai ( Exod 24:16 ). (http://www.biblestudytools.com/dictionaries/bakers-evangelical-dictionary/theophany.html)