I can not help you, I do not do clients, but I can think of so many what if situations for that scenario it is scary.
IMO, you chould only take on that situation during the 5th to 8th month of the clients fiscal year. Let the firm that made the annual accounting be associated with the federal and state filings. And you should get a back up copy ahead of time so you can run a quick audit to see what if any problems there are, and whether or not amended returns are going to be necessary.
And if you do take the client on, I suggest you first burn his back up file to a CD and file it away as a CYA kind of thing against future audits.
the incomng client needs to prove to you that he is current in his fees to the losing firm. In the old QB forum we saw several people asking how to get their file from the accountant when he refused to turn it over, almost always it revloved around the client being in arrears in his payments as the reason they were refusing.
The more I think about this the more I am certain that I would never use a "full service" accountant, where I was not in control of the accounting.
Have you considered having a get together of the local firms and bring this up? Other professions certainly collude in different areas, real estate being the major one.