Mautic - Salesforce CRM plugin
This plugin can push a contact to Salesforce CRM when a contact makes some action. If you don't have the Salesforce CRM account yet, create it.
Requirements
SSH. Your Mautic instance nas to run on https. Salesforce will not allow you to create App with just http callback URL.
Get the Salesforce client credentials
There is an official documentation about how to get the Key and secret although it doesn't seem to be updated.
Go to: Setup (tom right corner) / Build (bottom left corner) - Create / Apps / Connected Apps / New

Create a new app like this:
Make sure the Selcected OAuth Scopes are Access and manage your fata (api) and Perform requests on your behalf at any time (refresh_token, offline_access).
Copy the Consumer Key and Secret.

Configure the Mautic Salesforce plugin
Insert the keys to the Mautic Salesforce plugin and authorize it.

Configure the field mapping.
Test the plugin
Follow these steps to test the integration.
Troubleshooting
Error: The REST API is not enabled for this Organization.
This means the API is not turned on in your Salesforce account. Read more