Complex sentence: Following Swamiji's death in 1902, she went into a depression which took her two years to overcome, after which she devoted the next four decades entirely to the cause of promoting the Vedantic ethos of the Swamiji.
Split into simpler sentences: Following Swamiji's death in 1902, she went into a depression which took two years for her to overcome. After this period, for over four decades she devoted herself entirely to the cause of promoting the Vedantic ethos of the Swamiji.