There are many extension and third party apps available to download Gmail messages as PDF. but are you are using Google Chrome browser you can save all Gmail messages as PDF without using any extension and third party apps.
- Sign in to your Gmail account on Chrome browser.
- Open your Gmail message which will have to save as PDF
- Then click the on the Print all icon . see below image
- Print dialogue window will open then Change print destination as Save as PDF
After you change Destination as Save as PDF, finally click Save button. That's all your email will be saved as PDF in your computer.