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.

'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 end
'beenden' and 'weiterführen' are opposites when something has already started. 'beenden' means that you finish something and no longer continue it. 'weiterführen' means that you keep going with it. Both words fit tasks, conversations, projects, or courses. If something is not supposed to continue, use 'beenden'; if it is supposed to go on, use 'weiterführen'.

Nach dem ersten Erfolg will das Team die Aktion weiterführen.
After the first success, the team wants to continue the campaign.
Sie beendet den Kurs nach der Prüfung.
She ends the course after the exam.