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Spoiler Text

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Hello

So my solution.

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Kalliope Side :

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//-- settings.yml file

# ---------------------------
# Rest API
# ---------------------------
rest_api:
  active: True
  port: 5000
  password_protected: False
  login: admin
  password: secret
  allowed_cors_origin: "*" 

active:True allows using the Rest API
password_protected: False allows anonymous connections
allowed_cors_origin: allows connections from other sites. This option is mandatory because the MM site is localhost:8080 and kalliope 127.0.0.1:5000

Concerning the brain.yml file

  - name: "repeat"
    signals:
      - order: "repeat after me {{sentence}}"
    neurons:
      - say:
          message: "{{sentence}}"

This synapse allows Kalliope repeat a sentence.

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Magic Mirror side :

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The following lines could be inserted in a module file

//-- Create the Request object.
const Http   = new XMLHttpRequest();

//-- Url to call fo our synapse.
const url    = 'http://localhost:5000/synapses/start/id/repeat';

//-- Build our data to send as parameters of our request.
var sent     = 'This is the text I want Kalliope repeat';    //-- You can modify it
var data     = {"parameters" : {'sentence':sent}};
var dataJson = JSON.stringify(data);

//-- Launch the request.                
Http.open("POST",url);
Http.setRequestHeader("Content-type","application/json");
Http.send(dataJson);

I hope to be clear :)
I mark the post as Solved.

Thank you a lot for your time and ideas.

Regards

Nicolas