Transferring from Plesk to cPanel - Duplicate POP E-mails

Hello, Sorry to bother you but I was hoping someone might be able to help with this one. We have two servers, a Plesk system and a cPanel one. We are migrating customers from the Plesk server to cPanel. We have just transferred over a couple of customers but have found an issue. The customers had POP e-mail accounts set up and therefore when they tried to connect over the weekend, their devices connected to the new server and downloaded a duplicate copy of the e-mails. Is there a way to stop this? I'm guessing not as their devices are seeing the new server and assuming that the e-mails have not been dowloaded already but I'm asking just-in-case there is something that I've missed. Kind regards James