It is perfectly appropriate to observe a deceased mother's birthday with a poem. Acknowledging that she has passed and commemorating her birthday shows that the person in mourning has successfully navigated the five stages of loss and grief.
Accepting the loss of a loved one and celebrating their life is the ultimate goal in the grieving process. Expressing one's feelings through poetry, journal writing or even music is a great outlet. There is no wrong way to observe the birthday of a deceased relative if it gives the grieving person a sense of peace. A great poem that could be used for such an occasion is "My Mother, My Angel" by Kathy J. Parenteau.