Is it permissible not to wash the private parts and the organs of ablution during ghusl from janabah if they were already washed at the beginning of the ghusl?

A Muslim begins by washing his private parts when performing ghusl (ritual bath), then performs ablution (wudu') as for prayer. This ablution is performed with the intention of fulfilling the sunnah of ghusl or removing minor ritual impurity. If he washes his private parts and the limbs of ablution with the intention of removing major ritual impurity (janabah), that suffices him from having to wash them again later. Beginning with ablution before ghusl is an independent sunnah, and it is permissible to suffice with washing the limbs of ablution within it without redoing them, provided that the intention of ghusl from janabah is present from the very first limb.