living in China with X visa and then switch it to Z type without leaving from China

Hello everyone,
I'm a non native speaker teaching English in Beijing and holding X type. Also i have 2 months before my X type will be expired. My new recruiter told me that they can help me to apply for Z type without leaving PRC and it will be valid for 3 months (!) to seek a residence permit. As they said, it's hard to get invitation letter for non native teachers and in this way there's no need for that letter. And it cost 7500RMB so they ask me to split the bill. Do you know anything about that? Is it actually Z type they're willing to help me for?

Thank you.