I could open the AppRequestsListener on my app for Android, invite friends and send them an app request. However, that app request never arrived until I found this answer that you have to tick App on Facebook in your Facebook app settings and enter a bogus-URL in the Canvas URL and Secure Canvas URL fields. I did that and then the notifications were received by the selected facebook-friends correctly.
However, right now upon clicking on the received app request just a blank page opens. whereas I want the app to redirect to this play store link of my Wingman app directly. From my feeling the most plausible solution would be to include the play store link in the Canvas URL and Secure canvas URL, however that just shows a blank page, too.
I don't understand why I didn't find anything, there must be so many iPhone/Android apps sending requests to facebook friends and then linking to the app store.