cleaned up

//send a welcome email when a user account is activated
add_action( 'bp_core_activated_user', 'bpdev_welcome_user_notification', 10, 3 );

function bpdev_welcome_user_notification( $user_id, $key = false, $user = false ) {

    if ( is_multisite() ) {
        return ;// we don't need it for multisite
    }
    //send the welcome mail to user
    //welcome message

    $welcome_email = __( 'Dear USER_DISPLAY_NAME,

How to retrieve the template from the other code that does not work ?

L\équipe @ SITE_NAME' );

    //get user details
    $user = get_userdata( $user_id );
    //get site name
    $site_name = 'Your Site Name here';
    //update the details in the welcome email
    $welcome_email = str_replace( 'USER_DISPLAY_NAME', $user->first_name, $welcome_email );
    $welcome_email = str_replace( 'SITE_NAME', $site_name, $welcome_email );
    $welcome_email = str_replace( 'USERNAME', $user->user_login, $welcome_email );
    $welcome_email = str_replace( 'LOGINLINK', wp_login_url(), $welcome_email );

    //from email
    $admin_email = 'contact@mysocialart.com';// get_site_option( '' );

    $from_name = $site_name . "<contact@mysocialart.com>" ;//from
    $message_headers =  array(
        'from'          => $from_name,
        'content-type'  => 'text/plain; charset='. get_option('blog_charset')
    );

    //EMAIL SUBJECT
    $subject = sprintf( __( '[MySocialArt] IMPORTANT: MODE EMPLOI A LIRE %1$s ' ), $site_name ) ;
    //SEND THE EMAIL
    wp_mail( $user->user_email, $subject, $welcome_email, $message_headers );

    return true;
}