I'm not sure about the specifics of your question, but if you've received an offer from a buyer, to verify their seriousness it is mandantory that they have included a bona fide preapproval letter from their lender. The lender should also be with a company that you are familiar with. Don't be afraid to ask for them for a preapproval from your own lender or to personally call their lender to verify. Most preapprovals are free, so this shouldn't be a problem.
Also, while not mandatory, an offer of earnest money would be helpful. If they have an immediate "investment", such as earnest money, then you know that first of all, they actually have some cash and second, that they are willing to risk that cash. (The definition of "earnest" is fervent, purposeful, determined, resolute, serious, sincere. Earnest implies having a purpose and being steadily and soberly eager in pursuing it.)
Hope this helps.