How to get ClusterItem inside InfoWindowClickListener?

Question

Good afternoon!
I have integrated Google Maps into my Android application and I have clustered points on the map. For this I created a separate class:

public class MyClusterItem implements ClusterItem {
    private final LatLng position;
    public final Integer vectorId;
    public List<String> types;

    public MyClusterItem(double lat, double lng, List<String> types, int vectorId) {
        position = new LatLng(lat, lng);
        this.types = types;
        this.vectorId = vectorId;
    }

    // some overrides

    public List<String> getTagCluster(){ return types;}

}

When creating a cluster object, I pass an array into it as a tag:

MyClusterItem newItem = new MyClusterItem(pointLoc.latitude, pointLoc.longitude, pointObj.types, vectorId);
clusterManager.addItem(newItem);

Also I have InfoWindowAdapter. I installed it like this:

map.setInfoWindowAdapter(new CustomInfoWindowAdapter(getContext(), map));
                map.setOnInfoWindowClickListener(marker -> {
                    // i need to get TAG here
                });

Only the object with the tag is passed to the InfoWindowAdapter, not MyClusterItem. How to get this tag inside InfoWindowClickListener?
P.S. My CustomClusterItemRenderer looks like this:

private class CustomClusterItemRenderer extends DefaultClusterRenderer<MyClusterItem> {

        public CustomClusterItemRenderer(Context context, GoogleMap map, ClusterManager<MyClusterItem> clusterManager) {
            super(context, map, clusterManager);


        }

        @Override
        protected void onBeforeClusterItemRendered(@NonNull MyClusterItem clusterItem, MarkerOptions markerOptions) {
            markerOptions.icon(bitmapDescriptorFromVector(getContext(), clusterItem.vectorId))
                    .title(clusterItem.getTitle());
        }
        

        private BitmapDescriptor bitmapDescriptorFromVector(Context context, int vectorResId) {
            //a lot of code
            return BitmapDescriptorFactory.fromBitmap(bitmap);
        }


    }

That is, if I could insert a tag using MarkerOptions, then it would work. But this is impossible. (i think so)