Will old apple mail messages still work?

I have att bundled with dish network on a DSL line for phone, internet, T.V. so it's finally cord cutting time.

I already have a new faster internet provider as well for the change over.

Question: when I discontinue service for the bundle and the DSL line goes away will I still be able to access my old mail messages in apple mail?

Or will that not be accessible at all?

Many of these messages have links to them that I would still like to be able to click on and get to that site. Will that still be possible?

Should it be moved before discontinuing service?

Any other suggestions/something I'm missing before discontinuing service?

Thanks.

Backup all your mail and linked contacts before making the switch. Once you remove an account from Mail it will likewise remove all the associated messages.

And create bookmarks of those links in the browser instead of needing to go find a piece of mail to get there.