2 questions:
1. If you do get some more info from your hired source, what are you going to do with it? Get him sacked? Not sure where that leaves you
2. If you’re found out even considering doing this I suspect you’ll find yourself sacked pretty damn fast and then will have to explain it to future employers.
There’s twice when I’ve had dishonest bosses (lying at work, not about personal matters) which was affecting my ability to be effective at work and both times I simply kept a diary of their contradictions and lies, ready to show HR if for any reason they tried to implicate me. I would suggest this is your best and most legal strategy…
Re your post about getting fed up with it, OP, both the people I refer to above had very very fast staff turnover ie: people just left. That’s your best strategy IMO…