Hola CarlosAlberto, debes utilizar los eventos OnDragDrop y OnDragOver de tu Edit y la propiedad DragMode de tus Labels en dmAutomatic.
Código Delphi
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procedure TDualListDlg.EditDragDrop(Sender, Source: TObject; X,
Y: Integer);
begin
if (Sender is TEdit) and (Source is TLabel) then
TEdit(Sender).Text := TLabel(Source).Caption;
end;
procedure TDualListDlg.EditDragOver(Sender, Source: TObject; X,
Y: Integer; State: TDragState; var Accept: Boolean);
begin
Accept := (Source is TLabel);
end;
Saluditos