Hello, I have to work on an old Joomla 2.5 site with K2 Version 2.5.4 . The ultimate goal is to upgrade to J 3.5 as well as to update K2 to the final version, however in the meanwhile I have to face some problems. In particular, I have two User Groups in K2, the Group A has full permissions while in Group B the option "Edit any item" is disabled. In addition, I have assigned group permissions for the same categories for Group A and Group B, the difference is that users of Group A can edit every K2 item in that categories while the users of Group B can edit only the K2 items which they own (i.e. they are authors) in that categories.
For simplicity, I work with two users, user A belongs to group A while user B belongs to group B. Finally, both users are in the same Joomla Group named "Registered". The problem is that when the user A from Group A edit a K2 item which is owned by user B then automatically the "Author" of this item is changed to "user A" and then user B losses the permissions for editing and saving. I have to locate the item as administrator and change manually the author again to "user B" in order to user B regain access. This solution however is not permanent and of course not satisfactory.

Thank you in advance for any assist, it is of great importance for me to fix it.

This will be solved by updating K2. 2.5.4 is really, really outdated.
Update to Joomla! 2.5.28 backup your template and update to K2 2.7 or K2 2.7.1 DEV and then after you have updated EVERYTHING finally uou can upgrade to 3.5.x.

ALWAYS keep backups in case something goes wrong.

Thank you for your response, at the time being however the update is not possible due to multiple hard coded parts in both cores of Joomla and K2. I am in the middle of the process of listing them among others. So, is anything else that would you propose?

This is a really outdated version, years before we switched to Github, so I do not think I can I assist you on finding the patch since there are a lot of core changes from 2.5.x to 2.7.x.
It has been 13 versions and almost 5 years.