To setup a custom e-mail for when someone clicks on forgot password, start by setting up a new push notification newsletter.

Design your newsletter and ensure you leverage the HAPI variables for specific elements in the message.
{@first_name:@} for their first name
{@login_url@} where we will place the login URL to reset the password.
to place your company's name

Once done, click on Schedule When to Send.

At the bottom, select Send Forgot Password Email and assign the trigger.

Now when someone clicks forgot password, it will send this e-mail template.