Is a back to back closing legal?

In and of itself it is perfectly legal.  Often as not, however, transactions done like that are being done to hide or implement something that is at least of questionable legality.  Without knowing the details and reasons for the two transactions, however, it is impossible to say if there's anything illegal or inappropriate in this particular case. As I said, there's nothing wrong with it without there being more to it.

Disclaimer:  The materials provided below are informational and should not be relied upon as legal advice.

Back to back transactions are legal, so long as each of the individual transactions is legal and the parties enter each transaction in good faith.