Is there an smooth foliation of the plane which is not smoothly equivalent to a foliation $dH=0$ where H is a harmonic function without critical values?

If the answer is negative then we conclude that every smooth foliation of the plane  satisfies the properties required in the following post

https://mathoverflow.net/questions/273635/finding-a-1-form-adapted-to-a-smooth-flow

In fact for the foliation $dH=0$ the $1\_$ form $\theta=H_y dx - H_x dy$ is the required form.