Give them a copy of the extension form and the address to mail it to. If you file it and they are underpaid and have penalties, they may try to blame you. That is harder if they complete the form themselves.

Also - It is easier(and potentially safer) to fire clients in December than Filing day. They could make an argument that this has been your arrangement for years, and they will be penalized as they can't find another preparer on the last day.