Just my hunch;
Putin wanted control over oligarchs, local and international that were beneficiaries of the various privatisations that were entered into post-Yeltsin and during his early tenure. There's a video of Putin berating Russian oligarchs and threatening "a Kordokovsky" on them if they moved monies overseas or engaged in undisclosed capital flight.
Browder and his chums, rubbing their hands in glee at the prospect of hoovering up lucrative state assets that their agents had identified ( Magnitsky at al), weren't too keen on Putin's assertiveness over their considerable investments. Beresovsky encouraged the globalist/bankster outrage by claiming Putin to be politically illegitimate, a ---------- and a provocateur that had murdered people in apartment bombings that were the pretext for Putin's ascent to power. Browder lent a hand to these media efforts to undermine Putin.
Virtually everyone who had business dealings with Beresovsky is either dead (Litvinenko and Beresovsky himself), has recanted and abandoned their opposition to Putin (Abrahmovitch) or fled to Israel (Deripaska).
Browder has found traction in the UK and US national assemblies with his gripes. He's a bit like the entrepreneurial version of Ahmed Chalabi.
A good question is why that should He be listened to beyond a court of law ? To such an extent that national policy is ring-fenced around this very particular business deal(s) gone wrong.