Evicting tenant who pre-paid last month

[Justin Johnson]

First time landlord here! First tenants in July. It was difficult to verify income because of cash paid construction jobs, but previous landlord confirmed they never missed a payment. They have been late three months in a row. Paid on time with a bad check all three times. First two times payment was made shortly after and additional fees paid. This month they have yet to pay. Because income wasn't verified we asked for first AND last month rent in addition to deposit. Can I send an eviction notice at this point for non-payment? Technically I am paid in full until the end of this month. Also, can I accept partial payment and still be able to evict? I'm a landlord in IL.