How to move a local copy of my mailbox to a new IMAP server? My mailbox has just been shut down without notice by my internet provider, because the internet connection had been cancelled some time ago. There is no way I can access it now, the IMAP server refuses the connection.

I just created a Gmail account to use as my new email.

I have a copy of most of my emails on my laptop, in the Mail app. Is there a way I can transfer these old emails to my new mailbox?

I read that there are ways to do an IMAP-to-IMAP copy with third-party software such as Thunderbird, but this is not possible for me as I lost access to the old IMAP server. I hope there is a way to upload the local copy of my old emails to my new mailbox.
The first idea I had: 

Can you just forward the emails to the new account? 
But that means some data is not right like the sender and the recipient.

So my other attempt:

To repeat your situation I used a software which blocks the Internet connection. And I was able to create a .mbox file. (the screenshot was taken later so the iCloud account is online again)



In mail app I imported the .mbox file as a local import.
Then I selected the mail and clicked move to and moved it to my other mail account.



I hope I could repeat your situation well, if not please tell me which steps not work for you. Maybe my answer is completely not working for you.
I think there are much cleaner ways to do your task with python scripts (like this, or that), but I think this solution is the easiest.