I've seen the records of which you speak. There is nothing that I have ever seen that connects Henry Briggs who was a member of the Company to the Henry Briggs who wrote the letter to his brother Thomas.There is also nothing that I have ever seen that links the Henry Briggs in Virginia to the Henry Briggs who lived in Surry County, Virginia in the mid 1600s.
If you find conclusive evidence of either of those connections, there are many Briggs descendants and researchers who would be very interested in your sources.
I have never found anything that even tells us whether or not Henry Briggs of the Company (the famous mathematician) ever married or had children.I've looked in the Company records that were published, through biographies of Henry Briggs, etc. and never found any leads at all.