Transitioning from Fund Accounting to ER

You'll need two things: (1) to show the drive that you really want to break in through knowing your shit, and (2) have a pleasant personality so that people you meet will want to help you.

1. Do independent learning - depending on how much you want the job, this ranges from scanning the news for the sector you want to get into, to following companies and knowing basic things like their net debt and current valuation, to building your own model from scratch and writing reports. I don't know how helpful fund accounting experience is in understanding how different items of financials flow through / impact one another, but nonetheless you'll need to know your shit if you want an offer.
2. Ask people out for coffee chats - have your story of "why research" tight, and be a generally nice person. Assume every coffee chat is a potential interview; you've done your prep and it's time to showcase what you know if technical questions / stock pitch questions come up. Sometimes you'd get the bonus of naturally clicking with the person you're talking to, and sometimes you won't.
3. Repeat until you break in - every time you fail is another learning experience.

Good luck.