I was wondering this myself, but if it is trivial then why hasn't the Taliban done it to shoot down Apaches/Chinooks in Afghanistan left right and centre?
This to me suggests it's not that trivial, as from what I've heard it's not that there aren't still a decent number of stingers in Afghanistan. I have read reports of the odd one being fired which may suggest the odd battery has been found that just about has enough charge to work perhaps but they seem to be few and far between - certainly not frequent enough that the Taliban has figured out how to power them consistently enough to be a threat.
It is trivial to rig up a battery pack for Stingers (and SA-7s). The problem with those systems is that they are ancient (as in technology wise) and fairly useless against modern combat platforms.
However, giving anybody new systems is just asking form them to be copied and manufacturing licenses provided to whoever will pay for them. Sadly, the articles in Wikipedia that I want to use as an example are woefully inaccurate. Suffice it to say, if certain groups (state and non-state actors) obtain some hardware, they can and will duplicate it and they don't care who they sell it to as long as they get paid.