Late 30-Day Notice to Vacate

[Steve Y.]

Hi fellow BP'ers,

So I recently acquired my first multi-family and inherited a problem tenant (a story for another time) who planned on moving out in January which she already moved out as of January 1 with no notice.  My property manager and I verbally told her in December and on January 1 to submit her 30-day notice asap as per her lease otherwise the lease continues. She ignored our suggestion and days go by.  Today, Jan 9, 2019 she hands her 30-day notice to vacate but she intentionally dated it Jan 1, 2019 and writes some verbiage on the letter with a reason for moving out due to some issue with a neighboring unit. Not a true story but none the less, she's making it sound like she was a victim of some sort.  Does this letter hold any validity in court? I'm not sure how to handle this. Has anyone been in a similar situation?

Also, she was not planning on paying her January rent since she moved out but we told her she had to pay for January otherwise we have to go through the eviction process.  She of course she did not pay her rent. So my PM served her her "demand for payment" and "eviction notice" on the 8th as per her lease.  Luckily I still have her security deposit. To make things more complicated, she's allowing her boyfriend to stay in the unit for reasons I have no idea. What can I legally do?  Move forward with the eviction process when the date is due even though she moved out already but her boyfriend is still there? He's not even on the lease.  How do I get rid of him?  Do I just wait this out, keep the security deposit, and hope her boyfriend moves out the end of the month? What a mess...  Any suggestions would be appreciated for this newbie investor.

Thanks!