Message [to Skype]:
So you got two or more devices with your Skype account. The syncing between them is straight up ridiculous.
Sometimes you get a message sent to you weeks ago on one device. For example, if you chat on device A and the contact keep chatting while your logging out, and you later log in (could be weeks later) on device B and that contact also log in, then the old conversation pops up, like it was a new one. And you don’t have any history synced between device A and B.
This shenanigans is very confusing and contra-communicative.
Thank you for contacting Skype Customer Service.
We understand that you are having synchronization issue with the Skype application. We would be more than glad to help you with your concern.
Regarding your concern, we don’t advise our customer to log in to multiple devices for it will affect the synchronization of the Skype account. Like what happened to your devices, there is a delay with it comes to receiving a message because of the synchronization.
Skype Customer Service