I don't know of a way to do this easily.There are a couple of options.
ServiceM8 does have an open API and you could pay someone to develop an integration that sends an email into ONTRAPORT, along with some automation in ONTRAPORT to get it sent to the client. But it would be a custom application and fairly complex.
They have a Zapier integration, and ONTRAPORT has one also, but their Zapier triggers and actions aren't going to do all of what you want. Zapier could create a new contact in ONTRAPORT when a new client is created in ServiceM8.
They also have a Gmail / Gsuite integration; I think that could be used with our IMAP Settings to record the text of emails you send to them from Gmail and responses they send back to your Gmail account into their ONTRAPORT Contact Log. But there's not a lot of tracking or automation possible with this; it's just a copy / paste type of thing to get the content in the Contact Log.