Co-GM can´t drag out my shared Monster Tokens.

I have most of D&D 5e books and share them in our game. Our Gamemaster has access to my books throught this sharing (I host the game, while he is technically co-gm.  However he keeps running into a problem that when he drag a Monster out on the map it appears as a Blue person token and not the monster token. It seem random. so sometimes he get the right token and other times its the Blue person token. 

Could you have your Co-DM supply a screenshot of the Compendium, right before dragging?  My guess, they still have access to the SRD version and they are grabbing the SRD rather than MM version of the creature. 

I think you might be right.  Any way to disable SRD versions?  

Just ignore them, they are marked as "SRD" on the right. For folks that own the non-SRD version the SRD version goes away.  It is my guess since your co-DM does not own the non-SRD version they are getting a combination of their access and yours.