I tryed to take field from my account with admin rights. And it was done right, owner changed via right-click. But earlier i tried to take field from account with regular user permissions (preciousstones.benefit.: true, preciousstones.whitelist.: true) and nothing happend. User, which gave field have same perms. I checked it again with another field. Only my admin account can take the ownership. I checked list of permissions and commands manual. Nothing about special permission to take ownership. Looks like a bug.

I don't think it's a bug, it's by design.
If you want any player on the server to be able to transfer ownership of a block,
give them this permission in your default permission list:

preciousstones.admin.setowner

Then any player can set ownerships, but not have the rest of the admin rights.

Okay, but one user with regular perms can give ownership by /ps changeowner, and another user with same perms can't take it. And no word about "Insuffisient permissions".
I think, if i give users permission to change owner, so anyone can take and give abilities, not just give ability, its strange.

Interesting, I'll look into it in a little while.

I havn't found someone to test this with yet sorry.
I did find this flag though (I didn't know about it)
So make sure the block you're using has this:
can-change-owner: true

Taking ownership doesn't work by permissions. It works by the name. So if you did a typo in the persons name while doing /ps changeowner then that person will not be able to take ownership. I have added an error message when a wrong person tries to take ownership of a block, that way he knows someone messed up:

You cannot take ownership of this field. It has been given to: [OwnerName]