Tenant transition with tenants that know each other - allow early move in?

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I'm a very small-scale landlord renting out a unit in my own duplex. Have been renting it for almost 10 years with no serious issues yet (knock on wood). I am currently transitioning between tenants where Tenant A (moving out after 2 years with no issues) referred and is the sibling of Tenant B. I screened Tenant B per usual, although they have the least rental history of anyone I've rented to and are getting a bit of the benefit of the doubt based on Tenant A having been good (plus they have a guarantor, the mother of both tenants).

Tenant A is moving out half a month before their year-long lease ends. They have paid the final month's rent. Tenant B will move in on the 1st of the next month (1 day after Tenant A's lease ends but half a month after Tenant A vacates). Because the two are related, it's created an awkward situation. Tenant A would like to leave some furniture behind for Tenant B, and also has said (in writing) that they give Tenant B permission to enter their unit to move things in during the last 2 weeks of their lease. Tenant B has not asked to stay in the unit prior to the lease, only to put belongings there. This still makes me uncomfortable because the apartment will have stuff from Tenant B inside before Tenant B's lease starts, but with Tenant A's lease going until the end of the month (and them having paid for it), I'm not sure what to do about it. Just curious what route others would take here. Can I even create an amendment to Tenant B's lease for the start date when the unit is already rented to Tenant A? I can theoretically hold off on returning Tenant A's security deposit until after the end of the month, but I don't know if that serves a real point.

A few small points - these tenants are basically kids (pretty new renters). And the apartment is an upper that's definitely tough to move into, so the furniture transfer does have some benefits (saves a lot of banging around/removing of doors from hinges/etc.). The apartment probably could use some cleaning beyond what Tenant A will do but doesn't need any serious work. (Tenant B has expressed being fine with the apartment in whatever condition their sibling leaves it.)