retrieving old emails from a previous host

I have a new client we are hosting their website for and we recently setup new mail accounts for their existing email addresses. They were using 1and1 and 1 of the employees was logging directly into the server to check his mail, using no email client. he is able to do the same thing with inmotion's servers but wants to know if there is a way to transfer, retrieve, his old inbox emails from the previous host to show up in his new inbox he created with inmotion?