"working in conjunction" is correct and usable in written English. You can use this phrase to describe two or more parts or people coming together to work together in order to achieve a common goal, such as "The two companies were working in conjunction to develop a new system."

"In conjunction with" is an idiom that denotes the act of combining or working together with something or someone else. It emphasizes the collaboration or partnership between different entities to achieve a common goal.

They generally mean the same thing, though "in conjunction with" isn't quite as specific as "in cooperation with". "To work in conjunction with somebody" is just a wordy way to say "to work together with somebody".