Legal Question in Real Estate Law in California

First, Florida law will probably apply, rather than California's. Next, timeshares fall into two kinds - those that are true real-property ownership interests, and those where the owner's rights are personal property arising out of contract, rather than deed. It sounds as though yours is in the former category, so that a deed (quitclaim or otherwise) would be an effective and appropriate transfer mechanism, but you should review your documents (do you have a recorded deed creating your interest?) to be sure. If your time at the property arises out of contract, its transferability may be restricted.

A third possible category is the so-called "contract for deed" whereby a buyer (vendee) of real property does not finally acquire title until a series of payments to the vendor has been made, per a purchase contract. These are more common in the eastern states than in California.

In any case, your starting point would be to review your purchase documentation to determine the following: (1) do I own real property (acquired by deed) or personal property (acquired by contract); (2) what transfer restrictions are applicable to me?: and (3) does my agreement with the seller specify the state law applicable?

Also, if the timeshare is not fully paid for, what would be my obligation to the lender if I transferred ownership?

You have to ask a FL attorney.