Edit: JavaMail 1.5.5 claims to support Android, so you shouldn't need anything else.
I've ported the latest JavaMail (1.5.4) to Android. It's available in Maven Central, just add the following to build.gradle
~~
compile 'eu.ocathain.com.sun.mail:javax.mail:1.5.4'
You can then follow the official tutorial.
Source code is available here: https://bitbucket.org/artbristol/javamail-forked-android