The relationship between a userID and transactionID created by that userID can not be transferred to a different userID. This is true for any documentation created by a userID (agreements, widgets and templates).
There are two solutions that you can investigate to help with the immediate problem:
Gain direct access by either aliasing the old Admin’s email to the new Admin, or change the email address on the userID to something the new Admin can use to recover the password.
If this userID is primarily used to create templates (vs sending and signing discrete agreements), we recommend setting up a functional email address (eg: AdobeSignAdmin@mycorp.dom) so ownership of the templates can roll to the next admin without any friction.
Note: Email addresses in Adobe Sign must be unique. You will not be able to change the email to another address that already exists in the system.
The second option, Advanced Account Sharing, is only be available to Enterprise customers. Advanced Sharing is complex, so it is recommended that you contact your Success Manager to discuss the option and get a trial account so you can evaluate the functionality.