Switching hosting: Best way to transfer emails?

So I’m switching the hosting for a client’s website, and I obviously want to preserve their old emails.

There’s about six of them that use the company hosting for their email, and I don’t know who uses webmail, or if not, what mail client(s) they use. So, I’d obviously rather not have to talk them each individually through backing up and restoring all of their emails, or worse, do it myself.

I’m wondering if there’s some way I can transfer the email files from their old host to the new one (I have access to both), so all they’d need to do is switch some account settings on their mail client, and they’d still have all of their old emails intact.

Is there anything like that, or am I just going to have to buck up and do them all individually?

Thanks :beer: