Passing processor-function in library for ESP AsyncWebServerRequest

I'm trying to include the ESPAsyncWebServer lib in an own C++ class/library. I'm struggling to pass the processor function when starting a server.

Same problem was discussed here: Calling member function by pointer Passing a function as a parameter within a class ...but I can't find the solution.

My code looks like this:

code.ino:

#include "SoftwareUpdater.h"

AsyncWebServer server(80);
SoftwareUpdater Updater(&server);

void setup() {
  Serial.begin(115200);
  Updater.initialise();
}

void loop() {
}

Softwareupdater.cpp:

#include "SoftwareUpdater.h"

SoftwareUpdater::SoftwareUpdater(AsyncWebServer *_server) {
  server = _server;
}

void SoftwareUpdater::initialise() {
  server->on("/manager", HTTP_GET, [](AsyncWebServerRequest *request) {
    request->send(SPIFFS, "/index.htm", String(), false, [&](const String &var) -> String {
      return processor(var);
    });
  });
  server->begin();
};

String SoftwareUpdater::processor(const String &var) {
  if (var == "var_manager") {
    return "text";
  }
};

Softwareupdater.h:

#ifndef SoftwareUpdater_h
#define SoftwareUpdater_h

#include "FS.h"
#include "SPIFFS.h"
#include <ESPAsyncWebServer.h>

class SoftwareUpdater {
private:
  void _setupAsyncServer();

public:
  AsyncWebServer *server;
  String processor(const String &var);

  SoftwareUpdater(AsyncWebServer *server);
  void initialise();
};

#endif

This is the error I get