PM rejects ideas then brings them back later as his own
The situation is me and my colleague, say 'Jak', report to the same manager, 'Dom', but 'Jak' has the title of project manager. I am more into Business Analysis. He (Jak) does not have any idea of his own, but when people (including me) send him ideas for better work and collaboration, he rejects them, but in a way that the person is not offended.
But after a few days, he tries the same ideas, ones that were formerly rejected, but he tries posing those ideas using different words, and if it works says to his manager that it was all his idea, and he says he has been thinking and working hard for the better side of the project, even while others are slacking. There is so much of "I" in this guy.
PM Creates conflict within the team
Jak also has poor management skills for a person of his work experience and does not know anything about software development, or people management, but he is the entitled PM for a Development intensive project. And to an extent, he knows his weakness! But his only modus operandi is to create conflict in between Development, QA, BA and let people fight.
For instance, when clients find a bug in a feature, the QA says this was not stated by BA, he asks QA to send a mail to my manager without my notice, but he asks that they put him in the CC or BCC. The same he did to me when I had certain issues with QA or DEV. It has gone to a state where the manager 'Dom' has formed a strong perception or a prejudice that 'Jak' is the only person working and all others are slacking and having all kinds of issues. Dom himself has said this to me in few meetings.
We've tried discussing issues with management
Its very obvious that this guy plays awesome office politics, and much ahead of the game. Any emails sent to Dom against Jak has backfired against the person who informed it, as the manager, Dom, has formed a strong perception, and 1x1 with Dom were futile.
How should we handle 'Jak', who takes credit for others' work and ideas? How can we convey this to Dom in a diplomatic and professional manner?
The team morale is extremely low and there is no trust within the team, which is working positively for Jak, as he has succeeded in creating FUD (Fear in complaining to anyone else, Uncertainty of the project, Doubt about self)
To clarify further, Dom is not involved in the project in a day-to-day basis, as he is a senior manager. But Dom has recently fired a couple of developers last week, thinking what Jak says is right, but very few know the politics here that the issue is not with the DEV, QA, BA performance but with this PM Jak.