cmonster.FollowCharacter(cEgo, 0, 20);
adding this after any event in any room will make cmonster character follow cEgo to other rooms.
You may need to tweak distance and eagerness to get it looking right.
Also FOLLOW_EXACTLY will put cmonster's x y the same as cEgo's x y (on top of!).
Both chars need to be on walkable areas i believe.
Check out FollowCharacter in the ags help file.
To stop cmonster following simply add:
cmonster.FollowCharacter(null);
You can of cause also do a check to find out if cmonster is following.