I don't know for sure what conditions Inzaghi put forward to Inter Milan, but if the condition is a salary increase as offered by Al Hilal, then Inzaghi needs to prove his ability by presenting the Champions League trophy this season.
The rumor is related to a salary increase, but even though it will not be as big as what Al Hilal offered, I am sure Inter will give him a salary increase, especially if they win the Champions League trophy.
Another rumor, another condition requested related to bringing in several players that Inzaghi wants. If the financial situation and competition in the transfer market are good enough, it should not be a problem to attract good players to come to Inter.
I think it is a fair thing, Simone Inzaghi has worked hard in the last three seasons, Inter Milan management should offer a salary increase and adequate financial support to their manager. Regardless of whether they will win the Champions League trophy or not, in fact those two things will greatly determine Simone Inzaghi future. The average age of Inter Milan's squad this season is 29.6, which of course requires Simone Inzaghi to rejuvenate his squad next season.