Go to the Places dashboard/locations page of the new account and select Add another business.
Enter the phone number for the existing claimed listing, select “find business information” and go through the process of editing the listing that Google displays.
Change as little as possible initially and be sure to keep name, address and phone number the same.
Google will require you to reverify but you will be the dominant controller of the listing. As the last to claim the listing most of your data will be given preference.
It is preferable to claim it with an email at your business domain so if there is a dispute in the future, you will be recognized as the authoritative listing holder.
There are some quirks in this process the most annoying being that categories and photos from the original claimed Places Dashboard will continue to show in the newly claimed listing when displayed in Places.
The other quirk is that if the other SEO firm wants to go in and update the record, the account’s data that has updated the listing last will show in Places. This can lead to some strange outcomes.
The optimal tactic would be for the business to get the login from their SEO but sometimes that just isn’t possible