I lived in MO from January through July working for a company in STL. I moved to MS and began working remotely for the same company in STL. How do I file MO and MS taxes?

The W-2 from my employer only shows state / local wages for MO but nothing for MS. I contacted my employer about this and they said that since MO tax rate is higher than MS tax rate that they don't need to file anything for MS but that I should talk to a tax advisor about what I need to file. Everything I've read indicates that telecommuting is counted for the state it is performed in which in my case would be MS. I'm trying to determine what I need to do to get my MO and MS taxes filed correctly.