She should study more diligently.
We use would with all three persons (first, second, third) to express a regular practice, a hypothetical, a preference, or a future in a past statement. Thus:
Each day, the police would form a perimeter around the White House.
He would write a book if he could.
We would like you to come to the party.
I said that I would complete the report later.
(future in a past statement)
If your colleagues insist on using should with the first person when they mean “would,” they are simply trying to sound British. Thus, they might say:
We should like you to come to the party.