Harry Potter may not have that much to go off of to connect to his parents but he does have a connection to their Patronuses in a very important way in the Harry Potter series.
When it comes to Harry Potter and his parents, there is a sadness that is always going to be associated with the lack of relationship. James and Lily Potter sacrificed their lives for their son and, in return, he suffered non-stop until he was almost as old as they were when they died.
It’s incredibly depressing and an aspect of this series that is hard for a lot of fans but there are little ways we can see Harry’s connection back to his parents still. Part of that is in his Patronus. When Harry is trapped, a Patronus of a stag appears and Harry, in some sense, thinks that it is his father there to save him and Sirius Black.
In reality, it’s just Harry using his Patronus with the Time Turner. But that understanding that Harry has the same Patronus as his father? That Snape chose Lily’s because he loved her? It leaves us with an understanding of how deep a connection to another human can go in the Harry Potter series.
It isn’t just about who you love but how far you’re willing to go for them and, in a lot of ways, how completely your life will turn to revolve around them and connect back to them. Harry will always have the same Patronus as his father and that connection is important for both Harry and us as fans.