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Is there any way to repair or replace the charging port on the Samsung galaxy 4?

Here is the Samsung Galaxy S4 Teardown vedio. You can get the charging port for your version at here. Hope them will help you.

Yes. Luckily the charging port is a modular component on the Galaxy S4, and can be replaced independently without the need to break out a soldering iron (like on the S3). A simple eBay search for “Galaxy S4 Charging Port” on eBay will bring up a slew of reliable sellers/suppliers: Here you go.