I agree with Mr. Wignall's and Ms. Ellis' responses--tell them to change the password temporarily for you, then change it back afterwards. I always tell clients that it's partly for MY protection, i.e. if they have someone else at their company who knows their login (or their login is hacked), I want a 0% chance that they think I might be the problem.
Also, you do NOT want to claim it under your own account:
- you would be artificially giving Google information that that account and other clients of yours might be co-owned, or co-managed (so, are any links between them really editorial?), and more importantly
- Google local search has more confidence in the listing being claimed by the real owner if the domain name of the email address claiming it = the domain name of the website (see this thread as well)