Normal landlord-tenant law applies to the termination of subleases. You are the landlord, the subtenant is your tenant.

As you have no lease, the termination of the month-to-month arrangement is governed by statute. A tenant must give not less than 28 days notice to end a tenancy, effective at the end of a rental period. See Wis. Statutes, Sec. 704.19. Termination is effective at the end of a rental period. Thus, notice given on April 1 would be effective as of April 30; notice given on April 10 would carry over into May and rent would be payable through the end of May.

Your tenant is not obligated to provide you with written notice. He told you he was moving out. He moved out. You have notice as of the date he announced his intention to move.