Hello Kerabo, I assume the car your friend has is a W123 280E ?
I think most (if not all) of the Mercedes K-Jetronic (CIS) equipped models don't have in-tank fuel pumps, they all run a Bosch in-line pump with a fuel accumulator and fuel filter (mounted in a carrier under the car close to the fuel tank). The only K-Jet cars I remember having an in-tank helper pump were Volvos (there are probably other OE's too).
From my own experience, K-Jet cars don't like sitting unused for long periods, as the fuel system can get gummed up with fuel varnish (especially the injectors, and the fuel distributor / metering head). Other K-Jet system components that can give issues if left sitting idle for long periods are the warm up regulator and auxiliary air valve. Vacuum leaks can also cause all sorts of problems. Having said all of that, K-Jet / CIS is generally super reliable when maintained as it's comparitavely simple mechanical system.
From your photos I'd suggest your friend consider a new set of injectors (they're still available from Bosch and relatively cheap). Check the control plunger isn't stuck on the fuel metering head (you would have to remove / demount it to check), check the fuel pump is supplying the correct pressure and the accumulator is OK (internal diaphragm fails and won't hold system pressure, more of a hot start issue though).
I think you already mentioned that you were going to check the fuel pump relay.
I have attached a couple of things that might assist a little re. your troubleshooting.
Good luck with it.