My wife and I had a similar problem. I have an iPhone 5S and she has the Samsung S4. Initially she was receiving my text messages and then suddenly her phone stopped receiving them. Based on the comments posted by others I went in to Settings/Messages/ and turned on "Send as SMS". Unfortunately, this did not resolve our problem.
As it turns out, the issue was with her phone. She "inadvertantly" fat fingered my number on her key pad and designated my number as Spam. (According to her, it is apparently easy to accidently designate a number as Spam without the users knowledge... so she says ;-)
The SOLUTION was as follows: On the S4 go to Messaging, press on the Entry in question and hold down the Entry for a few seconds and a pop up will appear with the following options -- Delete, View Contact, and Spam. Choose remove from Spam (if available). Note, if your number is not listed as Spam then this option will not appear and in which case this comment likely won't help you.