The mandate is not owned by the group.
A parliamentary group helps organise shared parliamentary work. Its members remain representatives of the whole people and, under Article 38, are not bound by orders or instructions. Changing groups therefore does not require personal approval from the head of state.
Politically, a switch can matter greatly: if a coalition has only a small margin above the required majority, departures may change that position. Whether the government still obtains enough votes in a particular ballot depends on how members actually vote.

The other three answers
Changing groups is not the same as losing parliamentary rights.
they may no longer participate in parliamentary sessions.
Membership of the Bundestag does not end merely because an MP changes groups. They may continue to attend parliamentary sittings.
the Federal President must give prior consent.
The Federal President does not have to give prior consent. A free mandate is not a group assignment administered by the head of state.
the voters of these members may vote again.
Voters do not automatically get another vote because an elected representative changes parliamentary groups.
Losing a majority and leaving office are different matters.
Not every switch deprives the government of its majority. Someone may move between opposition groups, or the groups supporting the government may retain enough seats despite a departure.
A constructive vote of no confidence under Article 67 requires electing a successor with a majority of all Bundestag members. Simply changing parliamentary groups does not replace that procedure.
Article 38(1) · Basic Law ↗Change of group: mandate remains, majorities may change.
Notice “can”: the answer describes a possible consequence.
Three words for this question
- der Fraktionswechselchange of parliamentary group
- An MP's move to another parliamentary group.
- das freie Mandatfree mandate
- MPs' independent position without legal subordination to orders or instructions.
- die Regierungsmehrheitgovernment majority
- The parliamentary majority on whose support the government can rely.
