There is a way to do both. If you have already taken Alon’s bet and won, you should have an option to invite him without having to do his scene. If you have unlocked it, it would appear right after you activate the automatic shot for the cannon [Let’s give it a try!]. Another way of doing it (and I don’t really remember how to unlock it) is get another option to appear when you get ready to [Sit down with your friends], the option being [duck under the table] in EARLY MORNING. That is another way to get the gem. I can share my route (with the options only so it doesn’t spoil) if you would like!