The Caldera Forms users add-on allows for user registration and login forms, and combined with the method described at Add Password Reset Link To Password Fields , it is possible to manage reset password link with the default WordPress form.
In the method described below, we use the
caldera_forms_mailer filter hook to send the reset password link via a Caldera Form. The email field in the form that determine the user, needs to be set as the email recipient in the main mailer (the recipients option under the email tab in the Form’s editor page).
Where Does This Code Go?
When using WordPress hooks to customize Caldera Forms or other plugins you should not modify the plugin files, or you will lose your changes when you update the plugin. Instead you should create a small plugin to hold the custom code. It's easy, learn how here.
Technically you can add the custom code to your theme's functions.php, but then you will not be able to change your theme and keep these customizations.