Question : Can a DNS server resolve one particular host to another network?

I have a project with a specific need to host the client's FTP services while making it appear as though the server is part of their domain.

Scenario - let's say:
The client has the domain client.com.  
My network is vendor.com
We are hosting a file transfer server (ftp over HTTPS, ssh too) on our network.  Let's call it ftp.vendor.com
It is very important to the client that when their visitors use the file transfer services it appears as ftp.client.com, never as ftp.vendor.com
Our name should never appear in the process.  

Therefore a simple redirect won't suffice.  I don't know enough about DNS to say whether they can simply define 'ftp' to point to our server's ip address.

Any suggestions?

Answer : Can a DNS server resolve one particular host to another network?

As you suspected, add a Host (A) record for "ftp.client.com" pointing to your own FTP server IP address.

If you want to test it before committing anything to DNS, add the same entry to your Hosts file and see if it works as you expect.

Chris