Ideas on how to create a multi-part form, where the form requires completion/approval by another user
All you need is D7 forms API if you are comfortable writing PHP. There are several ways you could go about it. One assumes that the e-mail address of User B is the same e-mail they used to create their Drupal account. You'll need to store the result of User A's submission in a database somehow. Depends if you are already storing data from the DB or not. If not you can use variable_set() to store the e-mail address in one of Drupal's core tables and then variable_get() to retrieve it.

The idea is to save whatever user A stores to the DB after filling out the form. In your form definition, at the top check to see if that value is there. If so, you know user A has completed his part, next step is to check the user accessing this form. If their e-mail address matches the e-mail supplied during user A's part then you display user B's part of the form.