How to obtain a copy of my iPhone 15 Pro Max invoice?

Apple Store Online -- If you purchased the iPhone from Apple's Online Store, you can chat with an Apple Specialist to locate the invoice to print. You can also search for the order and print it from there also. Scroll down to "See where your order is" for the link.

Apple Store - Find a Store -- If you purchased the iPhone from an Apple Store, locate the store using this site and ask them for a copy.

If you bought it at a reseller, you must contact them for a copy of the invoice

The invoice information for retail and online stores is at:

Viewing & Changing Orders - Shopping Help - Apple

View or Print Invoice

"Once an item is shipped or picked up, Apple will create an invoice for your order. To view or print your invoice, go to your Order Listing page and select an item to go to the order details. Then, select View Invoice at the top of your order details page to access your invoice.

If you need help viewing or printing your invoice, speak with an Apple Specialist" Telephone numbers --> Contact Apple for support and service - Apple Support

I would provide links and telephone numbers but they depend upon the country settings you are using. It is best if you just go to the document yourself.

I can't see that there is any way to log in to an account

You didn't purchase it using the account that you are using to post here? Use that information to sign in.