You absolutely can not publish this without permission. It doesn't matter if you make no money off of it. Putting something in the public domain doesn't it make it better (and might make it worse).
Your friend was the sole copyright holder (I assume) when he was alive. When he died, the work did not stop having a copyright holder. The new copyright holder is the person he designated. If he did not designate someone, then it is his next of kin.
His spouse is first, then his child, then his parents, then his siblings, then other relatives. This is the legal order and note that only legal relationships count, not unmarried partners, not chosen siblings. (At least where I live...the order may be different elsewhere but the basic idea is the same.)
If you get permission from the copyright holder to go ahead, I recommend also asking anyone very close to him who might care (like an unmarried partner).
Put the permission in writing. Do not rely on goodwill or people's memories. Be very clear exactly what you're asking for and what will happen to any money that might come out of it. Create a page, print out two copies, sign both copies. One copy goes to the copyright holder, the other one goes to you after the other party has signed it.
The best you can get is a full transfer of copyright to you for all of the works in your possession. Ask for that, but settle for less.
I recommend the following steps:
- Go through everything your friend gave you and make a full inventory.
- Find out who owns the copyright.
- Have an informal conversation with the copyright holder.
- Create a contract and have it signed.
- Alter and submit the work as you desire, in accordance with the terms of the contract.