I remember someone saying (not sure which episode, though probably the same) that Eren lost his 3D Maneuver Gear after exiting his Titan form. I also remember seeing that myself, after exiting his titan form every time except the 2nd time he does (He had no gear on him, then, to begin with). So how was the girl inside the Female Titan able to have 3D Maneuver Gear on her, as well as a Survey Corps coat?
Note: I have finished watching the anime, but I have not read the manga. Please don't post any spoilers for me. Thank you :)
As mirroroftruth has already kindly linked, it is speculated by Erwin that someone who is talented with their titan ability may be able to regain their human form with minimal exhaustion. This means that, with appropriate planning or fortuitous circumstances at transformation, the controller (pilot?) could quickly change clothes or equipment using the transformation itself as cover. This is possibly shown by the Colossal Titan in earlier episodes:
or by the female titan herself during the carnage of her body being eaten. So she may not come out of the titan already wearing the 3D-gear, but instead may have picked up a nearby set.
To be clear, the female titan (Annie) and other titan shifters are not capable of shifting and not damaging the maneuver gear. In other words, she had the whole place ready with maneuver gears and was already wearing the coat\jacket before she shifted. It was also obvious that she managed to sneak in the Survey Corps because she was already wearing the coat\jacket.
I think it was also stated somewhere that after shifting a few times, it is possible to control damage done to your clothing. That being said, the Female Titan has had to shift a few times, so she could take precautions when doing so.
if they'd prepared maneuver gear in advance" it is not necessary they were be holding gear in titan form, they could prepare somewhere or get from the dead army, we know female titan had planned it , so she might have prepared gear for those case.