A 'pro justicia' is a kind of summons or notice that is served on a person, indicating that a matter has entered the arena of legal proceedings - either because a person is being prosecuted for some reason, or to put them on notice that if they do not take certain action, they will eventually be prosecuted/sued.

Sorry not to be more precise with the terminology, but this term does not appear in any of my legal dictionaries, for some reason, although it does appear in various places on the Web. I have not seen any strong evidence to suggest that it exists as a phrase in English or is recognised in English law.