We are using Thunderbird as our email client software and we will send our clients emails directly through Thundebird.

Is there a way so that when we send a customer an email via Thunderbird that it can land in their contact profile chatter?  

So like say I have a customer "donna@company1.com" and she appears as a contact in "company1" profile.  So what I want is that every time i send Donna an email (via Thunderbird) it will be captured in the customer profile of that companies chatter. 

So Hubspot has a similar functionality, if you see what I mean.  

https://knowledge.hubspot.com/connected-email/log-email-in-your-crm-with-the-bcc-or-forwarding-address

So if we send an email through our email client we want the eventual email message to end up here: