可是 is a two-syllable turn-word at a clause seam; 可以 is permission/ability before a verb. The 是 vs 以 second char splits them.
✗ 雖然他有錢。 → ✓ 雖然他有錢,可是… (the 雖然 grant needs the 可是 turn to land)
✗ 他有錢可是很小氣。 → ✓ 他有錢,可是很小氣。 (可是 opens the second clause; a comma sits before it)
✗ 雖然他沒有錢,可是他很快樂。當作重點是「沒錢」 → ✓ 雖然他很快樂,可是他沒有錢。 (the point that holds goes after 可是; don't put the throwaway grant there)
English lets "although" stand alone with no second connector ("Although he's poor, he's happy"). Chinese keeps the pivot 可是 even when 雖然 is present; 雖然 is the droppable one, not 可是.