You might not have got the right kind of serial mouse, there were several protocols. I am not even sure Microsoft had a serial mouse until a few years later, they had bus mouse mice. References to MS mouse in pre 1990 almost always mean Mouse Systems not Microsoft.

I found this info on
http://actapricot.org/history/apricot_review_1.html
at the very bottom part 1 (Hardware), a few lines above part "System Software".

Well this would have to be the mouse known to work https://web.archive.org/web/20150316132221/ht … greeneyed.shtml

Journalist must have got one of the serial ones in for review, can't find stated the exact period of time between only being a bus mouse in early 1983 and it being recognised that microsoft had serial compatible mice later in the 80s.

I don't know how you are certain to get a mouse 100% compatible with the earlier Microsoft ones, I do suspect that protocol switching mice, that support mouse systems, logitech, microsoft by autoswitching (though that usually depended on how the driver prodded it when it loaded) will be trouble.

Thanks for the reference; is something new for me!
So I will probably look for an Apricot mouse. But if I can still find it somewhere?!...
I can control the arrow (mouse pointer) with the numeric keys, but then the arrow 'jumps' so far that I can't get it on the 'disc' symbol...
Frustrating...

The usual convention was that mouse movement was slow on the cursor keys unless a modifier was pressed, and then it would either speed up linearly or take bigger steps, so maybe tap at the shift, alt and control keys hard in case one hung up.

First this: you were absolutely right. The shift key made the pointer take a smaller step 1 or 2 times.
But I was also misled by the keyboard. There is a small key with the word 'enter' on it (at the numeric keys) , and a large key with the symbol <--.
To format a floppy disk, the large arrow key does not work; the small one with 'enter' on it does. Special...
Thanks again for your quick help!