Share app with 3D touch context menu defined When you 3D touch on a springboard icon you’ll either see a short list of developer defined controls, or you’ll see a generic “Share appname” control. 

However, is it possible to share an installed app with 3D touch?
Or one would have to go find the app in appstore in order to share it?

For example, I want to share the music app, but when I 3D touch on it I only see some music I’ve played
The Music app is part of iOS and cannot be shared from the 3D Touch menu. Third-party apps show the share option in the 3D Touch menu, but first-party preinstalled apps do not.