Is it permissible for me to obtain financial support from the university by submitting recent invoices for previous purchases that I have already made to cover research expenses, knowing that the employee will submit invoices from a company I have not dealt with, and will request a sum of money in return for that, and what is the ruling on the money obtained in this case?

Grants and aid are not deserved unless the conditions of the granting entity are met. If the university only disburses funds to those who submit recent invoices, it is not permissible to obtain them through deception, falsifying invoices, or offering bribes. If the granting entity does not object to disbursing the grant for previous purchases, then explain the true situation to them so they can guide you to the correct way to obtain it.