Retailers don’t actively monitor this but Amazon has an issue with this.
Here is the dropshipping policy on Amazon:
https://www.amazon.com/gp/help/customer/display.html?ie=UTF8&nodeId=20180843018
You can dropship but it can never be apparent that it came from another retailer.
It is nearly impossible to do so if you go to a retailer’s website and place an order through their site to ship to an Amazon customer.
I would not do this on Amazon.