Over on the Pictoselector blog there is a new post about sending an email using the Indy HTTP components via a PHP script on a server. The post is not specifically about Delphi XE5 Firemonkey but the same idea applies if you want to send an email from a mobile app on Android or IOS. Should be no problem using the same idea in Delphi XE6 and AppMethod. The demo source code itself even uses VCL I think but there is nothing tied to any Windows platform controls and you should be able to easily convert the project to a mobile Firemonkey project. The general idea is that sending email locally from your device or desktop component can run into all kinds of problems with firewalls and your ISP. A better alternative is to connect to a script on a server and send the email from the web server. This example is pretty basic and if you were implementing it in a mobile app what you would want to do would be to have a login system on the server side where the user would login and then you would send the email for whatever action you needed to based on the user that was logged in. In any event this is a really code proof of concept sample that shows posting data to a PHP script from a Delphi client.
Head over and read the full blog post about sending email via a PHP script from a Delphi XE5 client.
Here is a mirror of the source code for the email sending Delphi client to PHP server.