Technically shouldn't do it but I'm with Stocky on this one, if anyone asks he can tell them he's going to look after a relative who's taken a turn for the worse, or something.
If you & him don't mind that he'll be staying with you for months, it sounds like he's better off in lockdown with you rather than his flatmate. The whole point of lockdown is reducing interactions & possible exposures; you might be opening up to one exposure but he'll be reducing his, so it makes sense overall.