Old topic, but I recently had to do this myself for some testing accounts.
Most email clients let you designate alternate send-from addresses for exactly this reason.
Anyone like OP’s user who’s employing forwarding email addresses should look into how to work with them.
In Gmail, for instance:
- Click Settings (gear icon)
- Click “See all settings”
- Under Accounts and Import…
- Edit Send mail as: [add your “aliases”]