one option is to use IMAP . Basically your e-mail will remain on the server of your e-mail provider and you have access to them with TB via IMAP. Other than that, a second option comes to my mind but it's definately much more complicated, less comfortable and I haven't tried it myself .Try this only if IMAP is NOT an option for you. You may syncronise the TB E-mail database with some cloud storage provider (like dropbox) on a regular bases. A good file sync tool is FreeFileSync (Open Source). The problem with this syncing method is that it can't look into e-mails and which side changed/deleted/etc. what. There are various disadvantages here which I can't get into more detail here. Better use IMAP.

The above answer is rather complicated for me. I was told once thata there is simply an option to be chosen in Thunderbird, and that it works!! Anybody knows?

yes, its certainly IMAP. See this website on how to set it up with Thunderbird: https://support.mozilla.org/en-US/kb/imap-synchronization

I am not educated enough to install the suggested, is there no simpler solution??

I'm not aware of any other solution. You may contact your e-mail provider and ask for help on how to setup IMAP. Sometimes they have step by step manuals (or a website) that will guide you through the process. I think that should be your best option. Check on the website of your e-mail provider if they have a help website or simply type in Google the providers name and IMAP.

I see, I will ask somebody to doit for me,thank you

one more rather simple idea, but it's certainly not as good as IMAP. Configure Thunderbird to leave the e-mails on the server after they have been downloaded. see also this website. As I said, the much better solution is IMAP. For example when you delete an e-mail on one PC it is also automatically deleted from the other PC as well.