Should I immediately sue my housemate for signing a lease with me and then 3 weeks later move to another state?

Question Details:

I signed a lease with 3other tenants. We agreed to pay the rent together. One of our housemates decided to move to out of state for 3 weeks after signing the lease. He promised us in writing that he would pay his share of the rent until we could find another housemate and sign a new lease (which the landlord agreed to do). However, since our negligent co-tenant agreed to live in a partition in the living room, we have had great difficulty finding a replacement housemate. He has not payed his portion of the rent this month. Can I immediately sue him for all his rent?

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