(Written previously: Phase 1: Getting to know each other)
Now you get to Phase 2: The best-behaved kid you can imagine. Once the kid has decided that you seem safe and nice, often they want to be as perfect and nice as they possibly can be. (At least the younger kids will; teenagers are more complex.)
In this phase, you are still full of adrenaline attempting to meet all those new parenting challenges that you hadn’t seen before even if you have raised kids before, like enrolling the kid in school if you aren’t the legal parent, like doctors’ visits if you don’t have the right to make certain medical decisions for the kid, like court dates, visits with birth parents and so forth. But fortunately, you think, this is a great kid, they are really easy to deal with, it’s stressful, but this is going to work out great! He or she is so nice and happy all the time!
My advice: enjoy, enjoy and enjoy! It won’t last. Things will change; in my experience about three months later, you get to Phase 3: Testing.