iPhone users don't send SMA (what we commonly call texts), they use iMessage, Apple's own invention. It sometimes works with SMS apps, it sometimes doesn't. It's a known problem and it won't be solved until Apple loses the attitude that if everyone else does it one way and Apple does it a different way, everyone else is wrong. (It gets worse if you had an iPhone and you ported to an Android phone without turning iMessage off - then all your "Apple texts" still go to your iMessage account, and no one ever sees them again.
There's nothing you can do other than, if you're going from iPhone to Android, you remove the iPhone from your iMessage account before you make any other changes.
