
fortführen
to continue
To carry on or continue an activity, conversation, or process that has already begun.
Wir werden die Diskussion in der nächsten Sitzung fortführen.
We will continue the discussion in the next meeting.
to continue / lead away
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to continue
To carry on or continue an activity, conversation, or process that has already begun.
Wir werden die Diskussion in der nächsten Sitzung fortführen.
We will continue the discussion in the next meeting.

to lead away
To lead someone or something away from a place. This meaning is rather formal or literary.
Der Polizist führte den Verdächtigen in Handschellen fort.
The police officer led the suspect away in handcuffs.
'Fortführen' (to continue / lead away) is a separable verb. The prefix 'fort-' comes at the end in a main clause. In subordinate clauses and in the infinitive with 'zu', the verb stays together.
Der neue Chef führt die Projekte seines Vorgängers fort.
The new boss continues his predecessor's projects.
The verb consists of the prefix 'fort-' (away, onward) and 'führen' (to lead). Depending on the context, it therefore means to 'lead something onward' (continue) or to 'lead someone away' (take away).
Lassen Sie uns das Gespräch nach der Pause fortführen.
Let us continue the conversation after the break.
In the meaning 'fortsetzen' (to continue), the verb is often used with abstract nouns. Typical combinations are 'eine Arbeit fortführen' (to continue a piece of work), 'eine Tradition fortführen' (to continue a tradition), or 'ein Projekt fortführen' (to continue a project).
Nach dem Tod des Gründers führten seine Kinder die Firma fort.
After the founder's death, his children continued the company.
You can recognize this meaning by the fact that a person or a movable object is the object. The context is often formal and describes an action by figures of authority such as the police.
Die Wachen führten den Gefangenen aus seiner Zelle fort.
The guards led the prisoner away from his cell.
to continue
fortsetzen and fortführen can both mean that an activity that has already begun continues. fortsetzen particularly suggests resuming something after an interruption; fortführen emphasizes more that the activity is carried on. The difference is a nuance, not a fixed distinction.

Auch während der schwierigen Phase führt die Gruppe ihre Arbeit fort.
The group continued its work even during the difficult phase.
Nach einer kurzen Pause setzt die Gruppe ihre Arbeit fort.
After a short break, the group continued its work.