Dear CAF,
I did as you requested in last post. I created new account, made login and waited until the screen locks.
Unfortunately behaviour was the same. After several clicks I got into panel.
@aleopo
Are you using gnome or kde?
gnome
I am just doing zypper dup after changes you wrote me. Will report the result.
OK friend;)
It helped. After zypper dup no matter if I use the screensaver or not I cannot enter without password.
Thank you CAF very much!
What can I say…? It’s a miracle 
I am so glad you got this fixed up. 
I am also very happy
I am complete newbie to Linux - I have switched to it some 2 month ago and I am very glad of it, although I do not come deeper to it than graphic shell. I still keep the old Win for safety reason, but actually I do not come back to it. For the two programs that require Windows I installed VM and they work perfect there.
Thank you for your support.
No worries. You are welcome;)