How does the poem define immortality?

I believe that this question is specifically asking about Sonnet 75 by Edmund Spenser. This is the sonnet that begins with "One day I wrote her name upon the strand." The speaker of the poem wrote the name of his lover in the sand, and the tidal waters washed it away. His female companion essentially tells him that actions are silly because the words will always be washed away. Additionally, she tells him that her life will essentially do the same thing when she dies.

"For I myself shall like to this decay, And eke my name be wiped out likewise."

The narrator of the poem responds by saying that he does have a way to immortalize the woman. He will do it by making her famous.

"Not so," (quod I) "let baser things devise To die in dust, but you shall live by fame:"

He will make her famous through his poetry that he plans to write about her. Her body may not live on forever, but her name will. To the poem's narrator, immortality can be achieved by having people always remember you.