Subdomain transfer from one host to domain on another host?

I am being put to the test by a friend to transfer a wordpress site on a subdomain on 1and1 hosting, to a domain on dreamhost. I have access to his 1and1 site(not ftp access), and ftp access to the domain on dreamhost, but I am having the most difficult time figuring out how to do the transfer. He would like me to figure this out on my own, which I’m sure includes asking around. Is it even possible to do it with the privileges I’ve listed above? Any help or even a lead is appreciated.