You can forward a whole chat - or case - from your External inbox to another team member.
To send the chat to another person:
Go to your Chat page
Open External inbox and click the chat you want to forward
Click Chat info icon in the top right corner of the chat's main dashboard. The Chat information window will appear on the right
Scroll to Forward Case option and click the arrow icon next to it. The new window will appear

Start typing the name of the person in the Search field or simply scroll and choose the contact from your list
Click ➕ button next to the person's name. The ✔ will appear
Click Forward case

It is also possible to just forward (a) specific message(s) instead of the whole chat. To learn more, review the Forward Message guide.