My bite is not aligned after Invisalign - the back teeth are the problem. Can the bite settle on its own? (photos)

My suggestion is to seek a second opinion from an orthodontist.  Ideally your back teeth need to align to allow for proper function and to take the blunt of the chewing force.  If your back teeth do not contact, more force is put on you front teeth which can cause excess wear, fracturing/chipping, tooth aches and jaw soreness.

It is possible for the your bite to settle on its own however in a limited time if after 3 months there is no difference i would suggest further orthodontic treatment. Wearing retainers covering up to the premolars will permit a passive eruption of the molars and help them to settle. Additional occlusal adjustment may be necessary. The use of a T-scan can help in determining in which areas of the mouth you might have pressure points that are possibly preventing the bite to settle properly. 

Normally the back teeth do not touch  just when you complete invisalign.  The plastic is just as thick in the back as it is in the front, so when you remove the trays and bite, because your jaws are a hinge, the front move further during the motion, and thus contact first.  Normally, you should go to nighttime wear on your last aligner and the bite will settle.  Your bite, however, looks a bit too open at the moment and likely requires either further aligners and attachments, rubberbands, or simply retaining the front teeth and let the back ones erupt for a while.  As to the correction of your crossbite, that would also help the open bite.  In any event, to deal with this you need to talk to the dentist.