Not by default, and as far as I know there aren't any released extensions on this website for this.
There is however the PM Spy
extension in development on Github you could keep an eye on.
Be aware though, it is discouraged to use this extension on a live board, it is only released for testing purposes! There could be bugs or other issues in the extension's code, since it has not been validated by the Extensions Team. Also, since the extension has not been released on phpBB.com, there is no place here to request support for this extension.
In addition, if you really want to read that one PM, you can look for it in the database where it is stored, but for it to really have a moderator or administrator module, you would need an extension.