This is a somewhat common situation, which can be split into two separate issues:
- What to do with the suggested edit?
- What to do with the "duplicate" user?
Handling Edits from Re-Registered/Anonymous Users
My personal opinion is that, in this case, since there is no way to know if the user suggesting the edit is the OP, one should reject the edit and say so in the "why I am rejecting this edit" textbox. Leaving a comment on the question, asking the user to login and edit the post would also be beneficial. Something like:
You are probably trying to edit this question as an anonymous guest or by re-registering as a new user. Please log in with your existing account INSERT_OP_NAME_HERE and click on the "edit" link at the bottom of the post.
Handling Duplicate/Re-Registered User Accounts
Only the Community Managers can merge accounts, and the request to do so should either come from the users themselves, or the moderators once they have confirmed that the accounts are duplicates and the owner wishes to merge them. As a regular user, all one can do is to tell the OP to ask a mod to merge their accounts if they wish to do so. We cannot, and should no, be actively checking for duplicate accounts.