Hi WayneCar11,
Thank you for posting in Microsoft Community.
I understand that it is very important for the Surface Earbuds to have a working charging case for the earbuds to serve it's purpose after charging.
The Surface earbuds should automatically pair to your replacement charging case. If you charge the charging case and put the earbuds inside the case, you should see an LED light fading in and out white while the case is plugged in.
If the case and the earbuds doesn't charge, make sure if the Surface Earbuds is up to date including its case. You may check this page for the steps to Update Surface Earbuds.
Let me know how this goes.