@remo You can verify the log shipment from Filebeat to Logstash without using Elasticsearch. Sometime if Elasticsearch is not working properly with Logstash then this kind of problem may arise.
You can verify it by following below steps:
Configure stdout in output section of logstash
[Note : If it is working fine then it is the problem regarding Elasticsearch and Logstash]
You can Follow the start sequence accordingly
Elasticsearch --> Logstash --> Filebeat