each of those points will/should have a number, might be on the side, but as long as those wires match the same on both ends it doesnt matter what colour the strands you use you will end up with a straight connection. your best bet at the other end is to get another keystone and wire it up identically but theres no reason why you cant get an easy fit plug and wire it like below, but again double check the original keystone is wired correct, the plugs and sockets are easy enough to connect, socket ends it just pushes in with a screwdriver if you get close to the retention points and push firm the wire bites in stripping itself as much as it needs and you can get some easy fit RJ45's that just snap down once you got all the wires set,
ah i scrolled past the first pic, didnt see there was more, thats a weird way to put it, the way its labelled up is confusing, they are generally just numbered 1-8. most of the time moulded into the plastic, the other side should show the other numbers so 4 5 8 7? im not sure why that one side has 2 layouts, unless it expects you to wire it crossover inside the wall. easiest thing to do is to terminate it to another box/socket/keystone numbered and coloured the same both ends and just use a normal pre built wire from appliance to the wall
ur socket looks wired up wrong to me, the first 2 should be swapped round the square is the solid colour wire and the circle represents the striped colour, it should match the colours on the side, but as long as you know and match things you will be fine, it will just be the next chump who doesnt check that will curse for hours lol from what i can see your solid orange is wired as 1, banded orange is 2, the rest all match up to the diagram below