If you're talking about progress in the single player campaign, game saves are stored locally on the console. To transfer them from your friend's PS4, plug in a USB-Stick or external hard drive and in the main console menu go to
Settings > Application Saved Data Management > Saved Data in System Storage > Copy to USB Storage Device
There, search for your Advanced Warfare save files and copy them to your storage device. Then plug it in to the other console and go to
Settings > Application Saved Data Management > Saved Data on USB Storage Device > Copy to System Storage
and copy the files onto your own console. It's important that you are signed in with your own PSN account when you copy the files from your friend's PS4, because according to the PS4 User's Guide you need to have signed in at least once with the same account you used when you copied the saved data.
If you have an active Playstation Plus subscription, you can also upload your save data to your cloud storage and download it on the other console. To do so, follow the same steps as above, but instead of copying onto a USB device, select "Upload to Online Storage" on your friend's console and "Saved Data in Online Storage" when copying the data to the other one.
If you're talking about online progress: Your multiplayer progress in Advanced Warfare is stored on game servers online and are automatically associated with your PSN account, so you don't need to transfer save data for it manually.
No
Games are tied to a specific account and are not transferable. Not only can you not transfer games from one account to another, you cannot transfer from a "master" account to one of it's "sub" accounts and visa versa.
In other words, if I bought a game, I could not give ownership to any of my child accounts. Nor could they gift me a game without first logging in with my account.
As for being free PS+ games, they are only free during the month they are offered. They have since gone back to normal price. Think of it as asking for a sale price months after the sale is over.
Best Answer
There is no official way to do this. Your worlds are tied to the save data of the account they were created on. Either use your old account or make a new world. Sorry that this doesn't much help, but there really isn't much you can do.