Regardless of who does the training, for such a thing can legally be outsourced, any airline operating under EASA rules must have a NP training. No if's, but's or when's. There is, however, nothing stopping an airline assigning multiple postholder hats to a single person, provided they can argue their case to the regulating NAA. With this in mind, the NP Training hat may well be hung on another NP, probably flight ops.
It's not the way I'd run a train set, but it's not illegal.