Should the amount spent on the school, which did not operate for a full year, be considered compensation for its sisters not receiving their salaries in previous years when they were working?

If the amount was disbursed to you as an entitlement, then you are permitted to dispose of it. However, if it was disbursed by mistake, it must be returned to the disbursing authority, unless your two sisters have a confirmed right with that authority which was denied. In that case, you may pay it to them if the entity that deposited the amount is the same entity that denied their right.