SMS Forwarder is safe, efficient utility that forwards all incoming SMS messages, missed calls and low battery notification to email addresses you configure.
SMS Forwarder supports only SSL encrypted SMTP, choose port 465 (default value, so can be omitted in configuration) or according to your SMTP server. If you want to use Gmail SMTP server for sending emails, you must configure your Gmail account to enable less secure apps (less secure means authentication via username and password in Google terminology). You can of course use any SMTP server (over SSL) of your liking.
Example settings for Gmail:
User name: your Gmail address
From email address: your Gmail address
Password: your Gmail password
Also enable less secure apps = authentication with username and password (this has been forced by Google, SMS Forwarder was previously "fully" secure app, but Google policy has changed):