we usually plan for this in the beginning, by putting some sort of attribute on our PMs and then making sure that this attribute has manage permissions to every project. E.g. by making your PMs all part of the same team, group or job role, and then putting manage permissions for that attribute into the project template it assures that all our PMs are able to manage each other's projects and that this permission is retroactive (so if a new PM arrives and is given that same attribute they have permissions to everything that started before they got here).
After this it's just a matter of making sure that they either have some sort of prompted report to find the projects they need to manage, or some sort of attribute-related dashboard (e.g. everything with my job role, group or team) that will pull up this information.