Th0mC the best solution will depend on that scheduler program, and I never heard of it before.
If that other app was based on Laravel, the easiest solution would be to add Passport to it, then use the Flarum Passport extension to use that other app as auth server, and voilà. But I don't think it's made with Laravel...
Then it depends if that other already has a built-in capability to act as auth client or server to see which option requires less work.
If it has no built-in capability for either, you'll need to implement it and no idea how much work that would be. You could either implement an oauth server in the planner and a simple oauth client in Flarum, or write Flarum as oauth server and planner as client, or use a third app based on Laravel Passport for all logins, and make both Flarum and the planner clients.
Do you know what auth capabilities that panner app offers ? Either as client or server.