If $225B is not correct then what is the correct amount that needs to be raised.
It's $75B in common equity. Check page 24 of the updated plan. Then $25B in new preferred stock and $67B in retained earnings, for a total capital build of $167B.
The lsat part is where I think Moelis is over-optimistic. The $67B comes over the course of 13 quarters (Q4 2018 through Q4 2021), but the presidential memo shows that the timeline is much shorter. Likely by the end of this year, so that's more like 3 quarters of retained earnings.
The warrant proceeds are not included in this for two reasons: the money doesn't go to FnF (so it doesn't build capital), and Treasury would sell its shares after everything is done. The same buyers that would buy Treasury's shares are the ones that would pay the price given for current common shareholders' shares as well. That isn't money that has to be raised at any point.