@erm67 @hund Mailpile... Interesting but too difficult for a quick solution in my case.
Thunderbird portable on a USB drive did the trick. I think I will backup an image of installation together with imported mbox file.
It is amazing how a proper email client is better than webmail for navigating through some 5000 emails.
I plan to use this only offline if anyone wondered.
10 - 15 years ago I took A Thunderbird mail folder, copied it from Win 98 to a Linux Computer, and then a year or so later copied it back to a Win XP partition, just to see if it would work, and it did.
But then I ditched all that for a Gmail account... and now it's time to ditch Gmail.
@paladin I would recommend downloading it all with OfflineIMAP. You could then sync it back to any email account you want to. And you have full readability.