I found this post where @dobey pointed out that the keyring seahorse-daemon/service must not run throughout the keyring data will be overwritten.
In order to that I did this steps:
Turn on the target computer but not log in or log out.
Use an other computer to log in to my NAS using ssh. Then changing to the backup folder:
user@nas:~$ cd <path to backup>
Copy the keyring data to the target computer using scp:
user@nas:<path to backup>$ scp -r home/user/.local/share/keyrings/ <user>@<target ip>:.local/share/
Login at the target computer. Open Seahorse/keyrings. The copied keyrings shall be listed now (or updated).
Sitenote Something I recognised first within my tests: Seahorse keyrings are password protected and they keep the password from the origin computer. In my case it was the same as the user login. It may a good idea from now to use a different one ;).
The unfavourable part at this way is, that it needs a second computer or a computer with at least two accounts. But in case that only one computer is available, it may work with temporally turn of the keyring deamon:
Search how the service is spelled correctly and get the PID:
user:~$ ps -u user | grep seahorse
user:~$ ps -u user | grep keyring
1234 ? 00:00:00 gnome-keyring-d
Stop the service by killing the process using the PID from above (1234):
Copy the keyring data as described above (or on a way you prefer more).
Start the service:
user:~$ /usr/bin/gnome-keyring-daemon --daemonize
The approach with
service gnome-keyring-daemon stop|start results in this error:
Failed to stop gnome-keyring-daemon.service: Unit gnome-keyring-daemon.service not loaded. That's why I choose the way above. You may provide a correct way to handle this.