He seems to have left it up to his staff, all of whom, strangely, were partisan Democrats and half of whom had direct ties to the Clinton campaign either financially or otherwise. Weissmann probably ran it and directed the writing of Book 2.
Link: https://thehill.com/opinion/white-house/454185-how-mueller-deputy-andrew-weissmanns-offer-to-an-oligarch-could-boomerang