You can easily convert emails in to PDF over email itself. There is an email based file called “conversion service” it will let you to convert email messages, web hyperlinks, office documents in to PDF files. It supports HTML and text mails.
Google chrome has an in-built PDF writer so it will be quite easy for you to convert emails (any messages) to a PDF file inside the browser itself. If you are checking/reading your email in mobile or tab, then you need some sort of PDF conversion app.
Other option to convert emails:
You can forward the original email message to email@example.com then that service will send a PDF version message back to you in a minute. I tried it by sending normal text message and HTML and the conversion was really perfect on both.
To convert the attachment files inside the emails, you can forward it to firstname.lastname@example.org and you will get back pdf format in a minute/ second.
There is one more service called zamzar that helps you to convert emails to pdf. But in PDFconvert.me you can convert just by forwarding mails and no need to visit their sites.
You can also use this service to conver webpages to PDFs. All you have to do is just send the web address / url of the page you want to convert in the body of email message to email@example.com and the service will send full page in the PDF format. This feature can be used for seeing pages that or else aren’t reachable due to internet filters.