I would like my co-workers to share their contacts information, so I'm able to contact this person my coworker spoke with, like a mutualized contacts directory.
Is that possible?
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If you use Gmail through your work, school, or other group, you can let an assistant in your organization manage your contacts. The assistant can then access your contacts to add names, update phone numbers, and maintain your addresses. You can delegate access to your contacts without granting access to your email or any other information in your account.
See the above link to learn the details.
Another alternative is to ask the G Suite administrator to add the external contacts to be shared to the Global Directory.
But the easiest could be to create a list of contacts on a spreadsheet and share it with your coworkers.
Since you are looking to share you Google Contacts or contact labels with colleagues, friends or family, Google currently doesn't have that feature.
There are some tools you can try: ShareEmailContacts.com Share Email Contacts allows you to Seamlessly share your Google Contacts or contacts across your team members and external domain users using your G Suite account. It syncs very fast and syncs across Outlook, mobile and tablet.
As I understand, you want to share your organisational contacts with your team/colleagues.
You can give ContactBook.App a try. ContactBook allows you to Seamlessly share organisational contacts across your team members using your G Suite account. It also Syncs with Multiple Devices, and allows admin to manage permission for each group/contacts.
I had the same problem. I wanted to share our client contacts with my team members but there is such facility provided by Google. My colleague did an intensive research but as per him, we had to do it by using external software to be able to manage and share contacts. We are currently using ContactBook So far its working great. I tried their free plan, it worked well so I went all in.