2 different Apple ID's on iPhone and Macbook Air

I just upgraded to a new Macbook Air, and transferred my data and account information over from my previous Macbook. In doing so, I was able to keep all of my documents and profile in settings to avoid having to set up everything from a blank slate. The issue I face now is accessing my iMessage on my Macbook. On my previous Macbook, I had my text messages synced to the device to be able to read and send messages from my Mac. This doesn't seem to have transferred over from my old Mac, and I'm not sure how to set it up again. All of my old messages have transferred over, but I can't log in to iMessage on the new Mac again. I tried forwarding texts from my phone to my Mac, but it has made no difference. I think the issue is that I have a different Apple ID on my iPhone and on my Mac. I'm not sure how this happened or how I was able to receive texts before with the different IDs. I'm not sure what to do now to be able to access my iMessages now on my Mac. I don't know how to change the Apple ID I am logged into on either device, but I don't want to delete all the data from either ID. Does anyone know how I can access my messages with the different Apple IDs, or have any other suggestions?