Single urgent occasion: consider escorted leave under section 98 StVG or interruption under section 99 StVG.
For a single urgent occasion the law offers two routes. Escorted leave (Ausfuehrung) under section 98 StVG means the prisoner is taken out of the institution under guard and supervision, for example to an unavoidable official appointment or a necessary treatment. Interruption of the sentence (Unterbrechung) under section 99 StVG goes further: it permits an absence of up to eight days, for example because of the serious illness or funeral of a close relative or another important family matter.
What to do now: First, document the occasion and its urgency (a medical certificate, a summons, a death certificate). Second, identify the suitable form, a short accompanied trip points to escorted leave, a multi-day occasion to interruption. Third, note that interruption requires secured accommodation and maintenance, that the prison governor (Anstaltsleitung) decides on approval, and that the enforcement court (Vollzugsgericht) decides whether the time counts towards the sentence.