I'm probably not the best qualified to answer that, but from what I have seen studying Java and Python (and JS I suppose) yes, they all share the same OOP principles.
OOP Design Patterns serve as a very good nomenclature across the languages.
Having said that, by the very nature of the environment in which it operates, some patterns are more frequently used in PHP and its worth tracking down the best and latest books aimed at it. I am not sure if there are new books any aimed specifically at PHP 5.3 or greater.
Going back to your original post, when your employers talks of OOP, perhaps they have in mind that they think you should be using an MVC framework? Deep-diving into OOP principles will of course set you up well to use an MVC framework to its best, but is certainly not a pre-requisite - which of course learning PHPs OOP syntax is.
I suspect that choice will depend on the nature of the work you do, and whether your day to day domain specific tasks and complexities will benefit from OOP practices, thinking and disciplines.
IMO all OOP study is good, and will make you a better programmer and also lead to the discovery of other "robust industry practices".
Here's a really good old post on learning OOP, which also amusingly cocks a snoot at my reply too.