As long as he hasn't gone to orbit. For example. If I play the whole raid until the boss. I unlock all 4 screens along the way. Then someone drops out and you take their place, then yes you'll get it when you activate the 5th.
If I did the same thing, but at the boss everyone quits and I go to orbit and start that checkpoint later then no.
It has to be done in one consecutive play through. People can come and go as long as someone is always there to keep it from ending so to speak. As long as one person stays the others can all leave to the tower for heavy and rejoin even, just as long as it never "ends" so to speak.
Does that help?
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Thank you very helpfull !