I have a few thousand files on my web site and would like them to be transferred
from my previous host to WestHost.
Is this possible?
If your question is "Could WestHost do it?" I think the answer would be no. You would need to backup the files to you own computer and then upload them to your WestHost account. If you have the ability to zip directories on your current host you could do that then upload the zipped file to the WestHost account and unzip it there.
Just to expand on what Shawn said, if you have the ability to zip files (via SSH, for example) on your old host, you could do that - putting all your files into sitebackup.zip (for example), and then with your WestHost SSH access, you could just do a wget to download the zip file straight from your old host. Then you just unzip and voila! That way, you don't need to download the zip file to your own computer and then re-upload to WestHost (a pain in the butt unless you have Broadband).