Yes, there is a way, using commands in the shell, or a combination of FTP client operations and a shell command.
First, you have to set the permissions on the “source” files so that the other user can copy the files. You can do this either with the chmod command in the shell, or with the facilities of your FTP client.
Second, log out of that account, and log into the “receiving” account as a “shell” user via SSH (not FTP).
Once there, use the shell’s “cp” command to copy the files from the one directory to the other.
The commans should look something like this:
cp /home/username1/domain1.tld/dir_path/filename(s) /home/username2/domain2.tld/dir_path/
You will need an SSH client to connect via the shell. There is a lot of help on some of this in the DH wiki - just search for users, SSH, and shell, and read the articles that you find.
You might consider that, if this is all new to you, it might actually be easier to just log into account 1 via FTP, download the files to your computer, and then log out of that ftp account, and into the other ftp account, and re-upload the files.