I'm guessing that y'all do not have any interest in him being a member. That might be the easy solution.
Moving on. From a fraternity perspective, my gut reaction is no as well. That he should not receive any of your proceeds. However, some sort of compensation should be arranged.
For example, if you were to use another space, then you would need to pay for the use.
So perhaps you agree on a set and small "usage" fee. This does not have to be monetary either. Maybe the chapter cleans the house for the semester (or year) as part of the agreement to hold functions there. Or perhaps y'all invite him to your general parties and he doesn't have to pay if you charge admission.
One additional piece of unsolicited advice.
Be careful with this. You do not want to put a wedge between the two members and their roommate. If this escalates in any way, you might not only loose the use of the apartment, but could cause hard feelings between all parties involved.
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