Hi Rachelle,
No, unfortunately it's extremely rare for Apple to reuse parts between different models of its phones. Some of the SE series phones do reuse parts from a previous model, but I don't know of any cases where you can use a part between a regular and a Plus or Max version. The lightning connector assembly for your phone is not compatible with the 13 Pro; you'll need one specifically made for the 13 Pro Max. Here are a couple that came up on a cursory search.
[link|https://repairpartsusa.com/products/iphone-13-pro-max-charging-port-connector-flex-cable-graphite|Apple :: iPhone Repair Parts :: iPhone 13 Pro Max Parts :: iPhone 13 Pro Max Charging Port Connector Flex Cable - Graphite|new_window=true]
[link|https://www.ebay.com/itm/255748472962|For Apple iPhone 13 Pro Max Dock Connector Charging Port Audio Jack Flex Cable|new_window=true]
Note that the charging port has a color option to match it to your phone; the first one listed is in the Graphite color, while the eBay listing has options for all available colors. You can use any of them, but there will be a color mismatch just inside the opening to the port that will be visible when the charger isn't plugged in.