Can a friend use the Monster Manual in my campaign?

So, in short, I created a campaign but it's my friend who is going to DM. I gave DM permission to him. If he buys the Monster Manual with his account, can he use it in this campaign?

Short answer is no. Longer answer is all purchased compendium based books are sharable by the game's creator not players or co-GMs..

I just did a search for a monster in a game that I am a player in, and I can see it. The creator of the account does not have the monster manual. Note that I am not a DM in the game, so I don't know if I could drag the monster onto the map, though. This begs the questions about me owning the players handbook, and the DM not. Are you suggesting that I cant use mine to level up my character?

When you buy a compendium, you always have access to it in games, even if you didn't create the game. As the creator of the game, you can also share your compendiums in it. If you share compendiums in your game, your friend would have access to any compendiums you own as well as the ones he has bought (the MM, for example). Edit to add: Your friend, however, would not be able to share his Monster Manual to other players in the game. As a GM, though, he would be able to drag/drop monsters from the compendium into the game.