I don't know based on the rulebook. The provided context explains that some bird cards have multiple habitat symbols, which means they can be played in any of those habitats. However, there is no information in the provided rulebook pages about moving a bird card to a different habitat after it has been played. The rules only describe placing a bird in a habitat when it is played (see page 4), but do not mention moving birds between habitats after placement. To answer this question definitively, the rulebook would need to specify whether or not birds can be moved after being played.

Source: Core Rulebook (pp. 1, 10, 4, 8, 9)