'conjunction' means 'combination or partnership'.

In simple terms, 'in conjunction with' simply means 'together with/in partnership with someone or something else'.

- Our company completed the project    in conjunction with/together with/in partnership with    a researcher from our local university.

Also, "in conjunction with" is not a phrasal verb.  "Conjunction" is not a verb in this context.  It's a noun.  "In" and "with" are prepositions.