There are other threads with this topic, and it seems to be a known issue for a long time already. I wanted to add my own thread to get it documented that we would like a solution to this problem as well.
I have many different mobile devices (Windows 10 phone, iOS phone, Android phones) and multiple Windows 10 desktop clients. It seems that if a mobile device is logged in to Skype for Business and is running in the background (while I am not using the device), if someone messages me and I am away from a PC that I am logged into Skype, I will get a message about 2-3 minutes after someone IM's me with a subject of Missed conversation with ..., and it has an incorrect time stamp of 2 hours before the IM was actually sent. We are in Central time.
Also, I have had an issue that I verified all of my Skype for Business mobile clients were completely shut down, but still received the Missed conversation with ... email. This normally doesn't happen if I am not logged into any of my mobile devices.
Desktop clients that I use are Outlook 2016 and Skype for Business 2016. We have others still using Outlook 2013 and Skype for Business 2015. Our mailboxes and users are in Office365 for both Exchange & Skype for Business.
The time of these conversations are correct when viewed in Skype for Business and it’s only the missed conversation emails that are incorrect.
Microsoft, please fix whatever is causing this from the mobile device side, and contact me for any troubleshooting that needs to be done.