The convenient way to achieve this without data loss is to use a dedicated tool to convert EML files to PDF. I had to convert some old EML emails to PDFs, but didn't want to do it all manually because there were too many files.
I tried a few options and then I used the TrustVare EML to PDF Converter. I liked that it can handle a lot of EML files without altering the original email text. The converted PDF format were the same style, subject lines and attachments. The layout was user friendly so I did not need technical knowledge to complete this. It quickly finishes the process and makes sure the emails are well organized in the PDF file.
Visit here: https://www.trustvare.com/eml/pdf/