I find your question so interesting because, ironically, Somerset Maugham's path to salvation is the fact that he is both the author and the narrator of the story! Why is this so? Well, even though Somerset Maugham only plays an extraneous role in the action, he is the one that has a more objective opinion, able to piece together all of the true stories from the words of the other characters. Because Somerset Maugham is an author by trade, all of the characters trust him with their deepest and darkest secrets; therefore, he is an ideal third person (almost) omniscient narrator!
A further reason for Somerset Maugham's path to salvation would be his intuition about people. Somerset Maugham has an avid ability to have insight into human nature and human personality. Look at his ability to delve into the character of Larry Darrell! No one else in the book seems to understand Larry, but Somerset Maugham's intuition allows him to see into Larry's personality and even his soul. Larry is always searching for answers, and Somerset Maugham is the first to realize this. Another example of Somerset Maugham's path to salvation is his intuition and insight. There is a reason why our narrator is so intuitive. The details are explained here:
For men and women are not only themselves; they are also the region in which they are born, the city apartment or farm in which they learnt to walk, the games they played as children, the old wives tales they overheard, the food they ate, the schools they attended, the sports they followed, the poets they read, and the God they believed in. It is all these things that have made them what they are, and these are the things that you can't come to know by hearsay
A good example of this intuition is his view on Elliot Templeton. Somerset Maugham provides comfort to Elliott when everyone else leaves him to rot. Somerset Maugham also pays for Sophie's funeral after he identifies her body. Perhaps the deeper aspect of Somerset Maugham's path to salvation would be the fact that he is absolutely NEVER judgmental about others.