HII have some experience with Farrand inductosyn transducers. I converted a 5 axis Mitsui Seiki machine 2 years ago. It had a dead Fanuc system 9 on it. The fanuc system did the conversion i assume to a digital signal on one of the cards, but i could not figure out that part.In the end i purchased two Farrand 220100 converters on Ebay, read the documents and it worked, but i must say it is not a simple setup.
Your photo above show the pre-amplifier. it amplifies the (very small) analog sin/cos signal before going to the converter board. there should be two of them if you want to use the 220100 converter. I met an experienced guy locally earlier this year who have been doing Fanuc and Siemens retrofits for 40 years, told me that the resolver converters will not work on these because they are "low inductance" I cannot say more about that though, a bit beyond my knowledge base.....
Attached is the manual for the Farrand 220100 i used. Note that you need to buy the connector card as well, not sure what the number is for that, there are some on Ebay, as well as 220100 cards. You also need a very stable 15, 0, -15V power supply for this.The 220100 card provides a 10KHz excitation signal, reads the amplified sin/cos feedback and interpolates them to provide a quad signal with z pulse.
Regards
Henk