The verb "to find" can be either simply or complexly transitive. That is to say, in the active voice, it can take a direct object as its sole argument or it can take a pair of arguments, that pair being an object and its complement.
The original sentence has a simply transitive "found". The direct object is a content clause.
Araucaria's response correctly claims that, at least in this case, the entire content clause is a poor choice for the subject of our intended passive voice construction. The cleft structure proposed in that answer is a sensible alternative.
However, extraposition is not the only option. "To find" can also be complexly transitive. The content clause can be split into two distinct arguments:
A recent study found [the practice of]* posting photos of oneself to correlate with lower levels of intimacy.
Here, the subject remains "a recent study", the verb remains "found", the object is the gerund phrase "posting photos of oneself" and the complement is the infinitive phrase "to correlate with lower levels of intimacy". Having split the subordinate clause into an object/complement pairing, we can now use the direct object of the active voice statement as the subject of a passive voice construction, leaving its complement in the predicate:
Posting photos of oneself was found [by/in a recent study] to correlate with lower levels of intimacy.
So, that's how you can link the last part. You allow the complement to stand as an argument of the passive verb.
From the perspective of your partial attempt, you extracted only a part of the active-voice verb's direct object -- the subject of the subordinate clause. What remained was a predicate.
As a predicate, "correlates with lower levels of intimacy" demands a subject. No such subject is available, since its original subject now belongs to the verb "was found". The reason that it demands a subject is that the verb form is finite -- it has a tense. Non-finite verb forms, in contrast, do not form predicates and do not require subjects.
The way to reattach this lonely predicate is to change its verb to a non-finite form, such as an infinitive, a gerund, or a participle. The resulting infinitive phrase "to correlate with lower levels of intimacy" can then serve as an argument of the passive-voice "was found".
* A gerund in this position is grammatically sound but potentially difficult to parse. Adding a common noun in this manner prevents garden-path readings. I do not mean to imply the existence of something like a null-headed noun phrase.