You will not be able to perfectly detect the e-mail client your users are using.
In E-Mail headers some programs choose to include the X-Mailer
tag, which tells you exactly with what program and version your user is sending the e-mail - of course that can be faked. Not all programs use the X-Mailer
tag, I e.g. couldn't find it in a mail sent with Microsoft Outlook 2010.
Besides that you could do some guesswork by the Received from
tag in the e-mail headers, but in the end you can use SMTP and POP3 with most webmailers like GMail or Yahoo. That means even though your e-mail is sent via servers from google.com, the originating client could still be Outlook or Thunderbird and not GMail itself.
Maybe we can help you if you better if you could tell us why exactly your client wants to know the programs the users use to read their mail? Probably to tune the appearance of newsletters?
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