Harmonic oscillation and Fourier
When you express the cosine as $\cos(2\pi f_kt)=\frac{1}{2}(\exp(j2\pi f_c t)+\exp(-j2\pi f_ct)$ and insert it into the convolution integral you get:

$$
h(t)*\cos(2\pi f_ct) = \frac{1}{2}(\exp(j2\pi f_ct)H(f_c)+\exp(-j2\pi f_ct)H(-f_c))
$$

In case your $h(t)$ is real-valued, you have $H(f_c)=H(-f_c)^*=|H(f_c)|\exp(j\phi)$, and you get
$$h(t)*\cos(2\pi f_ct)=\cos(2\pi f_ct+\phi)|H(f_c)|.$$

In case you have a complex impulse response, this does not hold.