I am not sure why POST method is preferable than GET since I don't know about API specification for the HTTP endpoint. Executing "curl -POST " actually does GET request. I believe we have to '-X' to specify HTTP method with curl:
when you are referring to download content from the URL, in general GET method is supported to get content from the webservice. I am not sure if you are configuring the POST request wrongly.
"HTTP error 405 method not allowed" means URL exists with webservice but you are not authorized to access/perform that action. Please check if you need to specify any authorization headers to perform the action.
I would suggest to get more details about the URL like uri, http method, is it ssl encrypted, any authorization fields required to access the URL etc and configure the Nifi processor to fulfill the same!