It is my belief that Ben Jonson knew that the author of the Shake-speare works was William Stanley.
Jonson believed himself to be the superior artist, and was in a career-long competition with Stanley, Jonson being the more competitive, Stanley the more conciliatory. This interaction of the two did not, of course, stop with the death of Shakspur, and the only relevance of Shakspur in this context was as the front-man for the works. Stanley required, and his friends supported, his anonymity. They—specifically Stanley, and the two dedicatees of the First Folio, William and Philip Herbert, Earls of Pembroke and Montgomery—employed Ben Jonson for his services in releasing the works of Shake-speare, thereby both making Jonson an ally in the deception and cementing the Stratford actor as their author. This Ben Jonson agreed to do, and did, but in such a way that he never positively identified the man from Stratford as the author. Worse, no doubt, from his employer's point-of-view, were the games he played with it, including referring to the author (albeit covertly) as still living. I think this is the reason John Dryden referred to Jonson's supposed praise of Shake-speare in the First Folio as "an insolent, sparing, and invidious panegyric", so at odds with the common understanding of Jonson's words.
Contrary to popular beliefs, Ben Jonson was neither praising Shake-speare, nor eulogizing him in his comments in the First Folio of Shakes-speare's works. Yet he had to appear to do both, and he succeeded to such an extent, that few people today realize he was in fact criticizing Shake-speare, who he knew was still alive.
In his First Folio comments, Ben Jonson says:
I, therefore will begin. Soule of the Age! The applause! delight! the wonder of our Stage!
For a good understanding of why this is derogatory, see Ben Jonson and Cervantes, by Yumiko Yamada, who makes it clear in her line-by-line analysis that this entire dedication by Jonson is a "false enconium", and that Jonson's opinion of the values of his age and its popular plays was that they were degraded, far removed from his more classical values. To call someone the soul of this degraded age was not, by any means, complimentary.
Thou art a Moniment, without a tombe, And art alive still, while thy Booke doth live,
Jonson does not say Shake-speare is dead. He says he is "alive still". He is explicit that Shake-speare is alive, but only implies that he is dead. Derby, of course, was still alive at this time.