"sen" can stand for "hänen" in spoken Finnish. The sentence decides its meaning.
"sen" is also an ordinary written word. Check the meaning note beside each example; not every use is a shortening.
Se ei vastannu, koska sen puhelin oli kii. - They didn't answer because their phone was off.
sen here: their - spoken 'hänen'
Written Finnish: Hän ei vastannut, koska hänen puhelimensa oli kiinni.
Mä lähetän sen sulle WhatsAppis. - I'll send it to you on WhatsApp.
sen here: it - object form of 'se'
Written Finnish: Minä lähetän sen sinulle WhatsAppissa.
Millon sen vois tulla kattomaan? - When could I come see it?
sen here: it - object form of 'se'
Written Finnish: Milloin sen voisi tulla katsomaan?
Mä otan sen. - I'll take it.
sen here: it - object form of 'se'
Written Finnish: Minä otan sen.
Junat oli myöhäs, sen takia mä en ehtiny. - The trains were late, that's why I didn't make it.
sen here: that - pairs with 'takia'
Written Finnish: Junat olivat myöhässä, sen takia minä en ehtinyt.
Mitä nopeempi, sen parempi. - The faster the better.
sen here: the (better) - pairs with 'mitä'
Written Finnish: Mitä nopeampi, sen parempi.
Spoken and written Finnish are different registers. The examples show how "sen" is used here and pair it with the written sentence. Learn the meaning in context rather than replacing every occurrence of a word.