Deactivated PSE 15 on old laptop but activation fails on new laptop, help please?

My old Windows 10 laptop, where I used PSE 15, broke down so I downloaded and installed PSE15 on my new Windows 10 laptop, using the link that I found here:

Installation appeared to run normally and my Licence Number/Serial Number was accepted.

I opened PSE15 on the new laptop, opened Photo Editor and it showed the following Error Message:

 

 

So I closed PSE15 on the new laptop and opened PSE15 on the old laptop, opened Photo Editor and went to Help -> Sign Out and signed out, as I am told that Sign Out is the same as Deactivate.

Then I closed  (but did not uninstall) PSE15 on the old laptop and opened PSE15 again on the new laptop, opened Photo Editor and it still gave me the same Error Message, see above. I tried several times and also tried Restart but it made no difference.

So I cannot use my PSE15 - help, please!

[For feedback that may be of interest - on the new laptop, during my PSE15 activation attempts, Adobe automatically updated Adobe Camera Raw with a new version. This is good for me because I use Adobe Camera Raw for editing my JPEGs - yes, JPEGs - far more than I use PhotoEditor.  Because everything that I usually need is on one simple page, and of course the performance of the critical Raise Shadows and Reduce Highlights functions are superb. A magic page.]

All the best from South West Midlands, UK!

Mike