For starters, signal retains a conversation for the length of time you grant. That can be indefinite. The way it is retained is in a local storage database. It is intentionally guarded against export (although this is somewhat unavoidable with backup features on phones), so as to avoid companies like Cellebrite making it easy for LE to overstep their bounds and pull the message database when they take your phone. If you want some kind of export interface, your best option is a screenshot — signal does not take any action that threatens the mutual security between parties as explicitly agreed.