After consulting a collegue the problem is detected. There is a bug in de source 'EmailHandler.Java'
After inserting an extra line the attachments are really attachted to the message:
{
log.trace("Process body part as ATTACHMENT");
// The content is an attachment
Attachment attach = new Attachment(this.context);
attach.setName(bodyPart.getFileName());
// START OF EXTRA CODE
attach.setAttachment_EmailMessage(mxMessage);
//END OF EXTRA CODE
Core.storeFileDocumentContent(this.context, attach.getMendixObject(), bodyPart.getInputStream());
attachmentList.add(attach);
}