Safe Haven

A frightened woman flees her house in Boston, having held a bloody knife. After taking shelter with her neighbor, she is shown moments later at the bus station trying to flee town. She buys a bus ticket with her hair now cropped and bleached and stops in the small town of Southport, North Carolina. At the general store, she introduces herself as Katie. After acquiring a job as a waitress and renting a small house on the edge of town, Katie Feldman (Julianne Hough) befriends her neighbor, Jo (Cobie Smulders) and meets Alex Wheatley (Josh Duhamel), a widowed father of two young children, Josh (Noah Lomax) and Lexie (Mimi Kirkland).
It's not too long before Katie and Alex start a relationship, and she becomes like a mother to Josh and Lexie. Meanwhile, Kevin Tierney (David Lyons), a Boston police detective, prepares wanted posters for a woman named "Erin" which describe that she is wanted for attempted murder. Alex sees Erin's wanted poster in the police station and notices the picture bears a striking resemblance to Katie. He confronts Katie with the information, causing a huge fight. They break up, and Katie moves out of her house.
As Katie is about to leave town, however, Alex intercepts her and says that he has fallen in love with her. Katie returns his love, and decides to stay in Southport. She tells Alex that she fled to Southport to escape her abusive and alcoholic husband. They got in a fight, and she stabbed him in self-defense before she fled south.
The Boston police detective, Kevin, is suspended for creating the wanted posters, whereupon it is revealed that he is Katie's (Erin's) abusive and alcoholic husband. Enraged, he breaks into Katie's former neighbor's home back in Boston and finds the phone number to the Southport restaurant where Katie works. Arriving just in time for the town's Fourth of July parade, a severely intoxicated Kevin sees Katie kissing Alex, which enrages him. That night, Katie has a dream that she is standing on the docks watching the fireworks when Jo comes up and tells Katie that "he" is here. Katie wakes up in the convenience store next to a sleeping Lexie when Kevin suddenly appears and confronts her, demanding that she go back with him. She refuses and tells him to leave. Kevin pulls a gun and pours gasoline all over the store, with the intent to burn it down.
When he hesitates, Katie buys time by faking sympathy for him and agreeing to return home with him. When he lets his guard down, she pushes him into the water; however, a firework spark lands on the gasoline, igniting a fire that engulfs the store. Alex sees the burning store, quickly makes his way across the lake by boat, and saves Lexie. Meanwhile, Katie tries to fight off Kevin; during the struggle, the gun goes off and kills Kevin.
In the aftermath of the fire, Alex recovers several letters which were written by his late wife before she died. The letters prepared ahead of time for memorable events such as Josh's eighteenth birthday and Lexie's wedding day. Alex gives Katie a letter with the words "To Her" on the envelope; the letter thanks the recipient for making Alex happy. Enclosed with the letter is a photo of Alex's late wife, whom Katie is astonished to discover was actually Jo.[clarification needed]This means that Jo was a ghost that led Katie to her husband, Alex.

Question: Who were the letters written by?
Answer: Alex's late wife