How to store in the database directly the translation?

I found the solution !
The problem was I loaded plugin domain only when plugins are loaded, not for the activation plugin.

It resolves my problem…

MyPLugin.php

class WPGroupSubs {
    public function __construct(){

        // Install needed components on plugin activation
        /* need to add this */
        register_activation_hook( __FILE__, array( $this, 'load_text_domain' ) ); 
        register_activation_hook( __FILE__, array( $this, 'install' ) );

       //Translation  when plugins are loaded
       add_action( 'plugins_loaded', array( $this, 'load_text_domain' ) );
      ...       
    }

    public function load_text_domain(){
            load_plugin_textdomain( $this->domain, false, plugin_basename( dirname( __FILE__ ) ) . '/translations' );

    }
}