Are the legally awarded sums in a case of arbitrary dismissal permissible for an employee, even if he did not work during that period?

It is not possible to definitively determine your entitlement to the funds without reviewing the terms of the contract between you and the institution. The contract is the reference point for such disputes, as the Prophet (peace be upon him) said: "Muslims are bound by their conditions, except for a condition that makes a forbidden thing lawful or a lawful thing forbidden."

If the entity that ruled in your favor is legitimate, then you are entitled to take what it has ruled. If it is not, then you must refer to the terms of the contract, and it is advisable to present the case to the Sharia courts in Sudan.