That is something I have done several times and the process is normally simple. You connect the phone to the laptop and Windows recognises it and asks where you want to save the photos and even if you want to delete them from the phone once the transfer is complete.
The snag is that she has over 2,000 photos stored on the SIM card i.e. NOT in the phone and therein lies the problem. Windows will recognise the pictures on the phone but not on the SIM card. There must be another way but it is very difficult to find an easy method.
You can buy SIM card readers that should do the job but they all seem to work with older versions of Windows and not the 8,1 that she has on the laptop.
I have no doubt there is a solution but it might not be quick and simple.
The lesson learnt is NOT to store too many photos or videos on any portable device without some sort of backup.A friend of ours had a similar situation with a digital camera. He could no longer take pictures because the memory card was full. When I enquired he had over 1,000 photos stored on the card. Just imagine if he lost the camera or the card became corrupt, he would have lost the lot. His solution was to buy another card rather than delete the photos he had. I hope that, at some point, he heeded my advice to transfer the photos he had to somewhere safer.
It only takes a few minutes to transfer pictures and video to a computer where you can keep them safe.In my case, the desktop I use has two drives which mirror each other. If one fails, as it inevitably will at some point, the other drive has an exact copy. For older pictures that are archived, I use a NAS box which again has two mirrored drives for the same reason.
Professionals go even further and save their work to several drives or media stored in different locations.
Of course, it all depends upon what importance you place on your photos. In the case of my daughter, they are memories of her family and friends that cannot be replaced. I hope we can find a solution, otherwise those memories could be lost for good.