Background : You have a private key in windows which is called your_private_key.ppk, and your public key is already deploied in the server. What you want to is make your private key works in linux instead of generating a new key and demand server admin to deply it again. So if you have the same situation, you have found the right place.
System : Ubuntu
Tool : putty-tools
sudo apt-get install putty-tools puttygen your_private_key_in_windows.ppk -O private-openssh -o your_private_key_in_linux.ssh ssh user_name@server_ip -i the_path_of_key/your_private_key_in_linux.ssh