I'll give it a try...
I'll start with the following assumptions:
- The second floor left jack is working for telephone while the right jack does not.
- The modem was installed on the first floor by the ISP's technician.
- You now want to move the modem to the second floor.
- All voice and data services are working properly.
- There are no other phone jacks.
As you said, the incoming blue and red wires are being fed down to the first floor. On the first floor, they are punched down on the first position of the upper terminal block. This is feeding the left jack and the beige modular cable. The beige cable feeds the DSL splitter with the combined voice and DSL signal.
The filtered telephone output of the DSL splitter feeds the black modular cable that is plugged into the right modular jack. Since the white and red wires are punched down on the first position of the lower terminal block, the white and red wires have filtered telephone service.
On the second floor, the white and red are punched down on the first position of the upper terminal block. This should give you working phone service on the second floor left jack. The right jack should have no phone service.
The yellow and red wires on the second floor are a mystery. Are there any other jacks in the residence? Do they work? If so there could be another complication.
The first floor jack has the modern color codes on the terminal strips that are the same as those for Ethernet connections. It's clear that they directly connect all eight wires to each jack. The second floor jack does not have the color codes. If the right jack works for phone service too and there are other working jacks in the residence, the second floor jack must be built differently.
If it has internal bridging connections, the second floor jack module may be unsuitable for the modem. Look in each jack and count the number of contacts. If there are less than eight contacts per jack, there must be bridging connections. Use a multimeter in resistance mode to check for common connections on the unused lower terminal strip. If both jacks work for phone service as connected right now, the jacks are bridged together. You will need to physically swap the first and second floor jack modules to move the modem.
If the second floor jack is not bridged and works the same way as the first floor jack, moving the modem is relatively simple. Pull the second floor white and red on the upper terminal strip and move them to the first position on the lower terminal strip. Cut the blue and red connection to the first floor and punch down the incoming blue and red on the first position of the upper terminal strip. Now the upstairs jack should work like the original first floor jack. Connect the modem and test the data and voice connections. The only difference would be that the first floor right jack is active for phone service while the left jack is unconnected.