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. (regular practice)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:
He would write a book if he could. (hypothetical)
We would like you to come to the party. (preference)
I said that I would complete the report later. (future in a past statement)
We should like you to come to the party.