Did they actually transfer the title of the real estate to the LLC? I'm puzzled how you can do that without the mortgage.

How should the transfer transactions record on LLC's book?

1. Record cost and original purchase date and accumulated depreciation at date of transfer?  Yes
2. How to record appreciation (FMV - Purchase Cost)? 704(c) built in gain-shows on the K-1

Is there any recording required for the market value of the property in excess of cost or basis on the date of transfer. Not if you're maintaining Cash Basis books.