I would imagine that, since this is the Advanced MUD Concepts forum, that anyone who actually implements such a feature will have a decent enough AI system to defeat simple PC work around tricks.

I would suggest that in creating the duplicate, the mirror automatically wears the best equipment the player has in inventory (to include containers).  What you decide is "best" is dependent on your game mechanics.  Some places value armor class over hitroll/damroll, other places do the opposite.  I also suggest that your mirror wield the weapon that has a) the best dice, or b) a decent race vulnerability exploiting damage type (i.e. if the player is a fire giant, and vulnerable to cold, and he has a cold damage weapon on him, the mirror uses that cold damage weapon).

If your players decide to start pulling other tricks, such as dropping their stuff, have your mirror immediately get everything on the ground upon creation.  They give their eq to a friend?  No problem, have your mirror create with the best equipment pulled from everybody on-line at the time.  Or, you could implement an "owner" flag for objects, and have ownership of objects cost something to change.

In the RP world, it may be easier to control your players without having to "hard code" these kinds of things.  I live in a PK world, so I don't have as much wiggle room.

Back to the original point, though.  It's really not that hard to develop a half decent AI system for anyone that's serious about having one.  Time consuming, perhaps, but hard...definitely not.