Unable to import module 'index': Error in aws cloud watch logs while using firebase-admin module - amazon-web-services

Question

I am trying to retrieve data from a firebase database when an alexa intent is triggered. Whereas everything is set up, the lambda function crashes as soon as I am requiring the firebase-admin module.
I am using the recommended way of authentication:
const admin = require('firebase-admin');
const serviceAccount = require("./{{GENERATED_JSON_FROM_FIREBASE}}.json");
admin.initializeApp({
credential: admin.credential.cert(serviceAccount),
databaseURL: "https://{{MY_FIREBASE}}.firebaseio.com"
});
Here's the error from CloudWatch:
Unable to import module 'index': Error
at Function.Module._resolveFilename (module.js:325:15)
at Function.Module._load (module.js:276:25)
at Module.require (module.js:353:17)
at require (internal/module.js:12:17)
at Object.<anonymous> (/var/task/node_modules/firebase-admin/node_modules/grpc/src/node/src/grpc_extension.js:30:15)
at Module._compile (module.js:409:26)
at Object.Module._extensions..js (module.js:416:10)
at Module.load (module.js:343:32)
at Function.Module._load (module.js:300:12)
at Module.require (module.js:353:17)
at require (internal/module.js:12:17)
END RequestId: 13504ee8-ac0a-11e7-bef6-2bc764d73bbe
Line 30 in grpc_extension.js says:
var binding = require(binding_path);
Any help for a total newbie?
EDIT:
As other solutions to similiar problems state, that false zipping may cause the error, I want to make clear, that I zip only the contents of my project folder by using the terminal
command zip -r myskill.zip *
Moreover I executed chmod -R 777 on the node_modules/ folder