I was pulling my hair out trying to figure out why I was seeing SMS delays no matter whether using the stock Messages program or other third-party SMS programs. After much time spent diagnosing this (including backing up, wiping, and reloading the phone), I finally figured out what was going on. I had not seen this solution anywhere on the internet. So I am offering it here in hopes that it will help others. I had read about making sure that power management was turned off for the messaging program(s), and I made sure that it was. But I have McAfee installed as my virus checker on my Galaxy S8+, and I finally came to realize that it was being power-managed. Once I turned off power management of the McAfee program, all the delays went away! Apparently, when the virus checker is hibernated, it is not awake to immediately respond to messages. Hence the delay. Making sure that your virus checker is not power-managed is the key to keeping it awake and responsive to messages!
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