Is it right to say (no colon here)"They have been moving permanently since the war" [STRIKE]Or[/STRIKE] or [STRIKE]is it:[/STRIKE] "They moved permanently since the war"?
[STRIKE]Or maybe[/STRIKE] Are both [STRIKE]are[/STRIKE] right?
Note my corrections above. Your first example sentence is OK if the people in question have constantly kept moving since the war. The second doesn't really work. You could say "They moved permanently after the war" or "They have moved permanently since the war". Those suggest that they probably once moved once and it happened sometime after the end of the war.