(Follow-up to this post.)
The following remarks are to be found in the Benjamin Kennicott's "annual accounts of the collation of Hebrew MSS of the Old Testament" from 1764, which you can read here:
As you can see, at least as of that writing his agent had failed to gain access to it. In fact, he never did gain access to it. He refers to the Aleppo Codex in the final product of his Bible search, the second volume of the Vetus Testamentum Hebraicum as "Halebi, apud Judaeos, Bibl. Heb.", listed among manuscripts he was unable to have examined.1
In the account from 1768 he refers to another manuscript whose home was in Aleppo at one point, but had formerly been in the Ramban's synagogue in Jerusalem:
Below you can read an interesting letter from an American Jew called Solomon Simpson about his father, Joseph (Sampson) Simpson's Hebrew Bible manuscript which he had loaned to Kennicott, as well as letters between the parties . It appears that this manuscript is the fruit of the inquiries made in America referred to in Kennicott's account from 1764:
Kennicott Solomon Simpson - Alexandria Advertise 07-13-1802
1 Not having seen the Vetus Testamentum Hebraicum (yet) I was able to glean this bit of information about how the Aleppo Codex is called from William McKanes 1977 article "Benjamin Kennicott: an Eighteenth-Century Researcher," in the Journal of Theological Studies.