While it is difficult to directly test the relay, its function isn't so difficult to analyse.
The simple way is to bypass its function. This involves jumping between the 87 and 30 terminals on the car. If the relay is the problem this should run the pump (it will do it instantly; without the key being on - be aware). With it running the car should start if this is your hypothesis.(fuel supply being the problem).
NOTE: the fact that the fuel pump runs and the car starts DOES NOT fully indict the relay as it has many inputs to be functional. All this test does is prove the hypothesis that power to the pump will run it and that with it running the car will start.
Turns out that the relay is such a common problem (almost always bad internal solder cracking) that doing this test probably infers a bad relay.
Owner 24 bay BSC
Bosch Master, ASE master L1
26 years MB technician