You should able to transfer accounts from your old server to this via WHM as follows. To work this properly you should able to SSH from this sever to the old server without any issue.
WHM login >> Main >> Transfers >> Copy multiple accounts/packages from another server
Here you need to provide the old server IP, SSH port, and root password.
If the above method fails you can transfer accounts manually as follows.
1. Take backup of the accounts using the following script: ( in source server)
# /scripts/pkgacct <account username>
This will create a backup file under /home with name cpmove-<username>.tar.gz
2. Copy(use scp) this file into the target server: (say 99..99.99.99)
# scp cpmove-<username>.tar.gz root@99..99.99.99:/home
3. Restore accounts using the following script:
# /scripts/restorepkg <account username>