I've just updated to lollipop on my Xperia Z1 Compact and have just realised no texts are coming in. I've just checked with a friend and they're receiving my texts but not vice versa. I've been using a text messenging app called Textra which is all working fine other than the main issue of not getting text messages. I've then tried to look at and hopefully use the original default messenger. It doesn't open just has a white screen with 'Messenger' at the top, so it then tells me it's not responding. Hope that's enough information, not sure what to do at the moment.
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You may also want to try some of the basics, such as removing the SIM card from the handset for a short period of time, once done see if messages can be received.
