Does this tenant have any grounds to make an argument in court to stay?

He has lived in the 2nd floor apartment for 2 months, he makes a lot of noise at night, constant arguing with his girlfriend who lives there, in which we had a verbal contract that it was only him, he later brought in this women. We addressed this issue & he denies she lives there despite it being true. When we asked him for the apartment back, he said he would take us to court & stay here for 3 to 6 months more, that he is comfortable & if he doesnt find anything within 1 month, which is the time we're giving him to leave, he said he will stay. This has me stressing out, I talked to a lawyer & he told me to write a notice of the discussion that took place & notifying him on paper that he has to leave by next month. We never had a lease agreement when he moved in, only verbal stating he was to vacate when we said so at any given time. Can he make any argument in court?? Thanks.
 
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