360 Game invites

this may help

https://beta.support.xbox.com/help/friends-social-activity/friends-groups/view-xbox-one-friends-on-xbox-360

On Xbox One, a friend is anyone you’ve added to your friends list. Adding new friends on Xbox One doesn’t require that they send a friend request first.
When you sign in to an Xbox One console, your Xbox 360 friends will automatically appear in your friends list, as well as in your followers list. If you accept a new friend
request sent from an Xbox 360 console, you’ll see them as both a friend and a follower on Xbox One.

However, friends who’ve been added on Xbox One won’t automatically show up on your Xbox 360 list. If you plan to play with them on your Xbox 360, you’ll have to send a friend request through your Xbox 360 console. Once they accept,
you’ll see them in your friends list on both of your consoles.

If you go into the 360 game menu on the xbox one you may be able to see this.

https://www.youtube.com/watch?v=q7YhbokEf2U&feature=emb_logo

Press start and select at the same time to bring up the xbox 360 menu.You can only bring up the xbox 360 menu while in a 360 game.

We are doing that, however when we send it (using the 360 menu) we don't receive any invites for a game or party.

I don't have a problem seeing my friend, I just can't get any game invites from him when using the 360 menu. Tried different games and restarting consoles. We can get xbox one game invites no problem.

I would recommend starting by testing if other accounts get a notification of the invite. And additionally are they already in the game? It's possible that it will not send an Xbox One notification of the invite, but just an Xbox 360 invite, so if they're
not already in the 360 emulation for the game, they might not see the invitation.

Test those things out and see if that changes. Let us know!