To the part of your question about changing ownership of ArcGIS Solution items when shared between two ArcGIS Solutions. This is not an issue. The items have already been deployed to your organization and are connected. The ArcGIS Solutions app will recognize deployed content within a single user’s content on deployment. So, moving will not be an issue with deployed ArcGIS Solutions.
However, if you want to deploy updates to that solution or new solutions that connect with a solution, the suggestion would be to deploy the updates or new ArcGIS Solutions with the user that owns the existing solutions (in your case the new user you are assigning the existing solution).
An additional note on moving an ArcGIS Solution from one user to another. I suggest creating a new folder with the name of the ArcGIS Solution within the new owner's content and then use the method Ayan mentioned to change the owner of all the items that come with the solution (in addition to the solution item). e.g., feature layers, hosted feature layer views, maps, apps.
