Apple Store in Shenzhen China Refused to Provide Apple Care+ Repair Service Bought on Apple Ireland website

Hi Guys, any suggestions or ideas will be welcome.

Problem: I ordered my iPhone 11 Pro on Apple Ireland official website along with the Apple Care+ service on 2019/09/22, the shipment notification (contains my order number, product details - phone and service, and my name) was sent to my Apple ID email address on 2019/10/09, and it said "the invoice will be sent after 2-3 days after the delivery", which I have never received. The Apple Care+ will be expired in a few days and I need to get the back of my phone fixed. I have made a reservation at the Apple Store in Shenzhen, China, but they refused to provide service for Apple Care+ repair, due to lack of proof of purchase.

My efforts:

1. The order has been made longer than 18 months, so that the self-service website doesn't include order history information.
2. I've enquired support on Apple Support app, and the customer service assured me that the invoice number will not be needed. Also, I've had my MacBook Pro and its Apple Care+, which was bought in Hong Kong, got repaired in Ireland as well.

My questions are as follows:

1. If it is possible for Apple Ireland to send me the invoice to my Apple ID email address? I'm sure I didn't receive it or mistakenly deleted it, because I have a separate email account for all my Apple stuff, and never manage things in it.
2. I assume based on the principal of equality, Apple Store in China should provide this service for my iPhone 11 Pro as well? Honestly, Apple service in other locations mentioned in this thread was, is, and might will be way better than service provided in China.
3. Also, I don't understand why the order history page get expired so soon, even before the service term ends?