in Vertretung in English: Indicates that a signatory is acting as the deputy of them who are qualified and responsible; distinct from im Auftrag (“per pro”), which merely indicates that the signatory has been instructed or authorized to sign.

Meanings

idiomaticIndicates that a signatory is acting as the deputy of them who are qualified and responsible; distinct from im Auftrag (“per pro”), which merely indicates that the signatory has been instructed or authorized to sign.
In Vertretung, Weber, Oberstudienrat.
Used other than figuratively or idiomatically: see in, Vertretung: by deputyship, proxy (in other contexts)