When any Person convicted of any Offence punishable upon summary Conviction by virtue of this Act shall have paid the Sum adjudged to be paid, together with Costs, under such Conviction, or shall have received a Remission thereof from the Crown, or the Lord Lieutenant or other Chief Governor of Ireland, or shall have suffered the Imprisonment awarded for Nonpayment thereof, or the Imprisonment awarded in the first instance, or shall have been so discharged from his Conviction by any Justice as aforesaid, he shall be released from all further or other Proceedings for the same Cause.