I’ve got the exact same problem but on the PS3 in UVHM. I’ve tried various things such as doing different missions first and saving and quits, entering Motherlessboard from other areas but no luck :(. I manage to complete this mission in both Normal Mode and TVHM without issue but for some reason in UVHM it’s totally bugged out and can’t be completed.
UPDATE 1: I managed to fix the problem . The key is to have this mission open then find someone online that hasn’t done it yet but ensure you pick up all the trophies and be the one that hands it in. Now I did it in Splitscreen on my PS3 but it should work in online Co-Op on the PC
UPDATE 2: It turns out that it was only a temp fix as I reset my Playthrough last night just for fun, speed ran the DLC back to the point where this mission became available and it’s glitched again . There is zero point anyone even attempting this mission whilst it’s so buggy so please Gearbox/2K, fix this bug.