
weiterführen
to continue
To continue or carry on something that has already been started.
Nach der Pause werden wir die Diskussion weiterführen.
After the break, we will continue the discussion.
to continue / to lead on
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to continue
To continue or carry on something that has already been started.
Nach der Pause werden wir die Diskussion weiterführen.
After the break, we will continue the discussion.

to lead on
To lead to a more distant or more advanced point. Often used as the participle 'weiterführend' (further/advanced), e.g. for schools or information.
Dieser schmale Pfad wird Sie direkt zum See weiterführen.
This narrow path will lead you on directly to the lake.
'Weiterführen' is a separable verb. In main clauses, the prefix 'weiter' comes at the end of the sentence. In subordinate clauses and in the infinitive with 'zu', the verb stays together.
Er führt das Familienunternehmen erfolgreich weiter.
He continues to run the family business successfully.
The verb is made up of the adverb 'weiter' (further/on/longer) and the verb 'führen' (to lead). The meaning is often literal: you lead something into the future or to a more distant point.
Wir führen das Gespräch nach der Kaffeepause weiter.
We will continue the conversation after the coffee break.
The present participle 'weiterführend' is very often used as an adjective. It then describes something that offers additional or more advanced information or routes.
Nach der Grundschule besuchen die Kinder eine weiterführende Schule.
After primary school, children attend a secondary school.
In the meaning 'fortsetzen' (to continue), 'weiterführen' is often used with abstract nouns. Typical combinations are: to continue a discussion, a conversation, a project, or a company.
Wer wird nach seiner Pensionierung das Geschäft weiterführen?
Who will continue the business after his retirement?
to continue / move on
Both words can express the continuation of a project or conversation. With weitergehen, the process itself is the focus. Weiterführen requires an object and emphasizes that someone actively continues or leads the thing that has already begun.

Nach der kurzen Pause führt das Team das Projekt wie geplant weiter.
After the short break, the team is continuing the project as planned.
Nach der kurzen Pause geht das Projekt wie geplant weiter.
After the short break, the project is continuing as planned.