Assuming you are limited to using ftp as you do not state that you have access using scp, the easiest thing is probably to use a tool such as ncftp on Server B to download the file from server A. Many command line tools exists for this, wget, curl, etc. etc.
This could later be automated via cron or some such if you need to do it periodically.
Tools such as scp or rsync with ssh are preferable as they encrypt the traffic and are (arguably) easier to setup for transferring entire directories. So you may want to first test and see if you can (on server B) run something like:
ssh usernameA@serverA # replace usernameA with the username and serverA with name/IP of serverA
and see if you can login. If you can, then you can use scp or rsync. If the link between the systems is slow or unreliable, rsync is preferable, can use command of the form:
(on server B to download the file)
rsync -a -v -z --partial usernameA@serverA:/path/to/file .
This will rsync the file from serverA as usernameA into your current working directory on serverB, and if the rsync is interrupted, running it a second time will restart from when the connection was lost.
-z adds compression, do not use if file already compressed to save a few cpu cycles
-a turns on a bunch of options, essentially says to copy things preserving everything about the file(datestamps, etc.)