Is it possible to detect rx+ rx- tx+ tx- wires with multimeter?

Call someone at the far away place and have them read out the color order to you. Or walk over there. The max length of the cable is 100m...not that much exercise.

Or better yet, cut that jack off and wire it properly.

If the pairs are in the wrong order the cable can still work, but will confuse the next guy. If they were not wired with pairs in the right places, you wont have "twisted pairs". That is essential for proper transmission, especially on longer runs.

A multimeter wont do you much good. A cable tester will. My fluke cable tester will try to establish a connection to the device on the other end on different combinations of pairs and report which ones worked.