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If you are trying to update the app, a request for another Apple ID password is often caused by updates to apps/purchases that were made when using the other ID. Those purchases are tied to the other ID and can't be transferred. One option is to delete the apps/purchases made by the other ID and download them using the new ID if desired. If necessary, check your purchases history to see which apps/purchases weren’t made by the current ID. 

Purchase History Review.   

See If you get an error when trying to activate iMessage or FaceTime https://support.apple.com/en-us/HT201422 Especially see the contact options in the document.

If you're using an iPhone, be sure contact your carrier to make sure that you can send and receive SMS messages.

Still not activated after a day? Contact Apple Support.

And you can get Apple telephone support for help in solving your problem using this link https://getsupport.apple.com/?caller=kbase&PGF=PGF63005&categhttps://support.apple.com/en-u

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And see If you can't send or receive messages on your iPhone, iPad, or iPod touch https://support.apple.com/en-us/HT204065

Please explain what you are doing to produce that outcome. What message is received when that outcome occurs?