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You must turn off iMessage before you switch phones. iPhones use a different system for text messages than other smartphones do. I think that it is a terrible design decision by Apple, but if you don't disable iMessage before you get rid of the iPhone/iPan, you may never be able to get texts from other people still inside the Apple universe. You should be able to just to into Settings>Messages and toggle iMessage off, but it does seem to always work properly. Business Insider has a very good guide on how to do it and make certain that it worked.
I followed your link and found another article there that was just posted on this topic that you might like. It is about Hillel Cooperman, an iOS app developer who experienced the same issue and brought it to Apple's attention at a high level, meaning Tim Cook. Despite it being elevated to "executive support" status for resolution Apple still hasn't fround a solution. The interesting point that Cooperman made was that most iOS developers never personally use Android products, so they don't really care. His proposed solution was to force 1/12 of Apple employees each month to use Andorid devices, and the problem would be resolved by the end of the second month.