I want to grant a user (username: paul) access to all directories shared by root with mod 770. I do it this way:

groups root
(here comes a list of groups in which root user is)

usermod -a -G group1 paul
usermod -a -G group2 paul
usermod -a -G group3 paul
...

All the 'group1', 'group2', 'group3' are seen in the group list of root user.

However, after adding 'paul' to all groups above, he still can not write to directories shared by root user with mod 770.

Did I do it wrongly?