multiprocessing: shared manager Pool fails with AttributeError

GitHub fields:

assignee = None
closed_at = None
created_at = <Date 2019-02-06.17:36:20.688>
labels = ['3.7', '3.8', 'type-bug', 'library', '3.9']
title = 'multiprocessing: shared manager Pool fails with AttributeError'
updated_at = <Date 2020-07-09.20:12:44.279>
user = 'https://github.com/giampaolo'

bugs.python.org fields:

activity = <Date 2020-07-09.20:12:44.279>
actor = 'Felipe A. Hernandez'
assignee = 'none'
closed = False
closed_date = None
closer = None
components = ['Library (Lib)']
creation = <Date 2019-02-06.17:36:20.688>
creator = 'giampaolo.rodola'
dependencies = []
files = []
hgrepos = []
issue_num = 35919
keywords = []
message_count = 2.0
messages = ['334962', '373427']
nosy_count = 4.0
nosy_names = ['pitrou', 'giampaolo.rodola', 'davin', 'Felipe A. Hernandez']
pr_nums = []
priority = 'normal'
resolution = None
stage = None
status = 'open'
superseder = None
type = 'behavior'
url = 'https://bugs.python.org/issue35919'
versions = ['Python 3.5', 'Python 3.6', 'Python 3.7', 'Python 3.8', 'Python 3.9']