Does the EU Long-Term Residence Permit let me move to other EU countries?

One main advantage of this status is mobility across the EU. As a long-term resident you can relocate to another member state to take up employment or self-employment, to undertake professional training, or for other purposes if you can show sufficient resources and health insurance.

This is not automatic free movement. You normally must submit an application in the new country within three months of arriving and meet that country's conditions. The Italian long-term permit gives you a strong starting position, but each member state still administers its own residence procedure.