If you want to synchronise folders and messages of an email account on several devices you should use the IMAP protocol on account set up.

Thank you, can you please provide more details (workflow) to make this adjustment?

If you are not familiar with the differences between email accounts set up using the POP or the IMAP protocol please consult this help article https://support.mozilla.org/en-US/kb/difference-between-imap-and-pop3 IMAP servers keep folders and messages on the server. An IMAP account set up in an email client on a desktop computer will automatically be synchronised with the same email address set up as IMAP account in another email client on another device, desktop or mobile. We need more details about your Thunderbird installations on desktop and on your mobile device to give further advice about how to gain synchronisation between them