A message saved outside of TB will always have the current date displayed in File Explorer, but if want to have the email's date shown in the file name, save the message with the ImportExportTools NG add-on (right-click, Save selected messages/EML format).

Thanks for pointing me to that Add-on!

I've installed it but I can't confirm that it solves my problem.

When saving an old e-mail of 2019/01/20, for example, it is now saved as '20190120-subject.eml'. But, as an EML, its timestamp still gets changed to the current date and time whenever I'm viewing it in the Explorer.

When searching the web, that issue seems to be a well-known Windows problem. Often the advice is given to exclude EML from the file indexing - but that doesn't work either. See...

www.sevenforums.com/browsers-mail/35334-eml-files-timestamps-updated-constantly.html

for example.

Any more ideas?

The add-on will only allow the email date to be added to the eml file name - it won't affect the date in the Explorer column. There's a further discussion here:

https://bugzilla.mozilla.org/show_bug.cgi?id=939519

I tried the method explained here on a W7 computer, but, unless I did something wrong, it had no effect. I'll try and see if it ca be done in W10.