Can they over take my H1B transfer from Company C to them during the H1B transfer process (RFE process)?

#1
I am working at “company A” thru Company C (Staffing Agency). I got a job at Company A thru company B (Staffing Agency). Company B work with “Company C “because “Company C” willing to work on my H1B transfer.
Company C filed my H1B transfer on October 24, 2018. I got an RFE on February 20 ,2019 with a reason of Specialty Occupation and Employer Employee relation. But I am working in the same field as my graduation degree (Working as Mechanical Design Engineer with MS in Mechanical Engineering).
My contract will be end on April 15 and the company “A” are willing to take me as Full time after that. They are willing sponsor for my visa. But I am the first one where they are planning to deal with this immigration case. So they don't the situation and I have to explain them what to do first ?
My questions are “Can they over take my H1B transfer from Company C to them during the H1B transfer process (RFE process)? So that I can tell my employer to go with H1B transfer? Otherwise I must tell them to extend my employment until my decision? I am having difficultly to deal with Company C to do my RFE response. They are just delaying it to response. ?
 
#2
Company A can file change of employer & give your previous employer's reference(prior to company C) AND need to clearly indicate change of employer petition was filed by company C, RFE issued & during all time you were employed by them, got paid supported by pay stubs.
 
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