how to synchronize contacts from desktop to smartphone android

The Thunderbird mobile app doesn't have it's own address book or sync mechanism for Android contacts. You will need to look into third party android apps.

If your email provider supports carddav, an app such as Davx5 might be a possible solution.

F-Droid: https://f-droid.org/packages/at.bitfire.davdroid/ Play store: https://play.google.com/store/apps/details?id=at.bitfire.davdroid&hl=en-US

The idea for a built-in address book has been requested by the community on mozilla connect. You can show support by voting for this, or raise your own ideas and suggestions.

https://connect.mozilla.org/t5/ideas/an-address-book-in-thunderbird-for-android/idi-p/84952

Thunderbird on Windows 11 has a tool called “Account Hub” that lets you add an address book.

Options:

1) Sync from an existing account

 2) Add remote address book

 3) Add LDAP address book

 4) New local Address Book

Settings…Composition…Addressing

Allows selecting “Local Address Books” and automatically adding outgoing email addresses.

“Account Hub” locates individual company address books and adds to or updates the Thunderbird address book.

Suggestion: Export “All Address Books” to a file for importing on a mobile device or other platforms.