We’ve previously walked you through how to import old emails from other clients to Gmail using IMAP, or you can do it using POP. However you imported your old mail,
Google support page runs you through how to set up Mail Fetcher. The last step is “Add Account”. At this point:
Olivier says this will let you use the “from:me” search in Gmail to look
for email you sent using any name or address – so you can find everything you sent from all your old addresses and aliases.
If you still want to send mail through Gmail which looks like it’s from your old email address you can set up a custom “From:” so that you can select this address in the “From” field when creating an email or reply in Gmail.
Tips for importing old email to Gmail [Official Google blog]