Can i put an app purchased on another apple id on to a new one?

Hi, I just got my dad's old iPhone 4 (because he just got a galaxy note 2) and I have never had an apple device before so I want to create my own apple id on a separate laptop to his. Now he has this satnav app that he paid money for and he says that I should put it on my phone as he has paid a lot of money for it and doesn't want to waste his money. I would like to know if there's anyway I can have it on my new iPhone even though it was downloaded on a different apple id as the one I want to create and use on the phone. If there's a way that you can transfer apps to a different id or even just download it onto the phone can you tell me please.

Thanks in advance, I appreciate your help

Added (1). How would I be able to download it from his account onto my phone. Do I just sign into his account on the app store app on the phone, and just find it and download it?

You can't transfer it to your account, but you can just download it from his account then make your own apple Id. Even without being signed in with his apple id, you'll still be able to use the app.

Just have him download it again with his apple id on the iPhone 4.It should tell you he has already purchased a previous version of the app and the update is free.

You will need to log out your apple id (or whoever's apple id is logged into iTunes) and log in your dad's. Then, download the app as normal.

EDIT:
About your new additional details: yes