Tenant Unresponsive and Unwilling to Update the Lease

[Larissa Castro]

We have a renter in our second unit that is on the lease with her ex-boyfriend, now they are separated and the brother is living there without being on the lease (Missouri). We tried to communicate with them to add the brother and remove the ex but every attempt has been ignored. We purchased the duplex a month ago and they came with it. 

1. What should we do next? 
2. Does the brother need to be on the lease?
3. Can we just stay in this current situation for another 6 months until the lease ends? Could we be sued in the future for discrimination if we allow this situation to continue for the next 6 months? 

They did pay the rent on time this month and have been paying for the past 6 months too. 

Thank you,