DotNet Web API Bypass to SharePoint API in Enterprise Environment

So I need to access SharePoint Rest API which has EndPoint as below

http://sharepoint/_api (Internal company domain)

for mobile application which can create list items and list tasks.

so the current setup is, There is a web api thats publicly available which can basically acts as proxy takes a requests from mobile and inserts in SharePoint lists using CSOM.

lets call web api as https://api.example.com/proxyapi/api/controller

What i want is basically web api controller to blindly redirect all the request coming to it to sharepoint rest api endpoint http://sharepoint/_api

with maintaining all the paths.

Example:

Request #1

https://api.example.com/proxy/api/controller/web/currentuser

should get response from http://sharepoint/_api/web/currentuser

including authentications and what not.