Yes, you can save contacts from Facebook Messenger from PC with InTouchApp Extension for Chrome & Firefox.
Before you proceed, you need InTouchApp installed on your phone & InTouchApp Extension installed on Chrome or Firefox. Learn more.
How to Save Contacts from Facebook:-
Step 1 - Log in to your Facebook account
Step 2 - Open the Messenger from the Left panel & navigate to the chat from where you want to save the contact.
Step 3 - When a contact number is being shared, you would see the magical Contact button to save the number.
Step 4 - Select the option - Add new contact/Add to existing & you would see a screen prefilled with the contact name, number & photo. You can fill in more details too & click on Save Contact.
The number gets automatically added to your phone contact book.