website transfer within Inmotion

I set up an account with InMotion about a year ago. I thought I was entitled to a free website transfer and that it had been done, but in checking my cPanel, I don't see the website files. I see that there is an option to transfer a website in the cPanel, however when clicking on where the website is coming from, it doesn't offer InMotion. The website is already with InMotion hosting with my old webs design person. I switched web designers and now need to move my website to my new account I created at InMotion. How do I do this if the web transfer module doesn't offer me the option to transfer from on Inmotion account to another.