No.

Or-at least not via more or less direct way, some short sectors-first and last can be done by train, if you really insist. With the sector in between (Huelva/ES-Ayamont=border town, cross river by ferry, walk about 2 KM to first PT-estacao: Tunes?-forgot this name). I´ve done that reverse long time ago, when there still was a very slow overnite train from Lisboa to that Tns, and before € came.

ON this site-find country information and it will show maps with the main railwaynetwork in the countries.

This will take most of the day-it will not connect.

Its far better to simply use the direct BUS, over the new bridge further inland. 2 trips/day, maybe more in hi-season. Use google: sites like rome2rio or omio will give more details.

The way all by train is up north (only 1/day) to Merida-stay overnite, next day shuttle to Elvas/PT, then on to Entroncamento?)-IC train to Lisboa, overnite, next day any of the comboios to Faro. You will  not want that, I guess.

Update- this first town in PT you reach this was is called Vila real (de San Antonio), not Tunes.

The direct bus is run by DAMAS from ES and Algarvebus.