No. As noted in the Lease Agreement, by the end of the lease, no later than 12noon on May 22nd, tenants must remove all debris, rubbish, personal belongings and discard all items from the apartment.
If you are selling or giving furniture, or other personal items, to someone who is moving into the apartment on or around June 6th, after their lease begins, they will need to put those items into storage for the period between the time you vacate the apartment and the new lease begins.
Any furniture or personal items left in the apartment after the apartment has been vacated is considered abandoned property. Section 55-248.38:1 of the VRLTA covers abandoned property.