To report my colleague to management for unprofessional behaviour ?

[SunConure]

So there have been redundancies in our department and also redeployments to lower grades. It’s been a stressful process but I recently found out I have kept my job. Unfortunately the person doing a similar job at the same grade has not kept hers. Perhaps naively, I tried to help her in various ways, we even discussed a job share. Now I find out from various colleagues that, on more than one occasion, she is going around telling all and sundry that I did not deserve to get the job as “she doesn’t know anything about
science” and “her research is not aligned to what the department wants” and “she shouldn’t even be in our team”. It’s making other colleagues uncomfortable to have to listen to this and one or two asked her to stop. AIBU to report her to management and ask them to deal with it? I could ignore it but the way she is trying to undermine me makes me think it needs nipping in the bud right now and also that management should know about it so they maybe think twice about redeploying her. She is always nice to my face and she doesn’t yet realise I know about how she’s behaving. I could bring it up with her but I know from experience she will deny,
minimise and pretend it was not as bad as it actually is.

retired manager here. I wouldn't go to HR about hearsay but raising it as "I have been told this" at your 121 is both sensible and reasonable.

In your shoes I would ask one or all of the people she has been badmouthing you to, to go to HR themselves and keep you out of it for now.

I have done this before for someone and the gobby one was moved and then let go at the next reshuffle.

Ask them to do this with no expectation obviously.

She could just argue that she is saying what she thinks. Maybe she could back up her assertions if pushed. Best to leave alone.

I get the impression that OP works in academia in which case HR really will not care.

Ah that changes things. I would definitely have a discussion with management in a how do we resolve this way. Although you could still take the initial suggestion and then when the outcome settles revisit it then. Stops you looking too harsh. I'd be surprised if management hadn't picked up on her embarrassing herself like this

I wouldn't report hearsay.
I also wouldn't get involved in he said she said and would be wary of colleagues who did. If they're uncomfortable they need to report it to management themselves instead of coming to you.

If reporting what she has said is slagging her off, that may have something to do with what she’s said? Think about it… the colleague on the other hand is sharing her personal, very negative opinions about the op, these two are very much not the same. One is bullying, one is responding to bullying.

I am not sure if what she has said counts as personal and you can't really stop people saying they don't think someone knows their job very well etc.

She’s bitter @SunConure , it’s all those sour grapes she’s been munching on. Keep your head down and your mouth shut, let it wash over you. They go low, you go high…not worth a second thought. Hope it all works out well for you.