In an update on Friday the EA said 414,000 user accounts have been successfully reconnected.
Ulster University is set to make up to 450 staff redundant as it tries to make savings of about £25m.
Nearly 50 small primary schools in County Tyrone have closed their doors over the last 20 years.
It is not clear which parts of the university, which has campuses in Belfast, Londonderry and Coleraine as well as in Qatar, will be affected.
The IT system used by schools, called C2K, was targeted in a cyber attack at the start of the school Easter break.
A mother says her son will start primary one at a disadvantage after he didn't get a space at a local pre-school.
The Education Authority says as of Tuesday morning about 80% of post-primary schools are back online.
An IT system called C2K, which provides all online and IT systems in NI schools, was targeted in a cyber attack.
In an update on Sunday, the EA said its teams had been working over the weekend to "restore access to the system safely and securely, starting with primary schools".
