Get two Mailboxes together?

a small question. I have a Mailbox and I get eMails via iMap (not pop). On my old ISP, there is the old Mailbox with all folders and emails. On my new isp is my old domain transfered from old ISP to new ISP and I have a new mailbox, with the new emails received.

I get all my Mails via Thunderbird. So I have at the moment two email boxes.

Now my question: If I get my old emails from the old ISP, get Thunderbird this folder structure and emails into it and put my old mails together with the new mailbox? Or delete Thunderbird some emails?

Hope I have described the problem to understand what I mean. My english isn’t so good. Sorry for that.

Thanks for any tips or answers.