Is the colour of a wave from a far galaxy the same for us as for a galaxy which lies between? Because of the expansion of the universe, light from a far galaxy is redshifted. The expansion of the universe will make the wavelength of light longer. But is the colour of such light the same for us, as for an galaxy which is between us and the far galaxy. 

I first thought that a further galaxy's speed was higher than ours, but I don't think that's right it is relative. But is the speed of the far galaxy from a view of the further galaxy higher than from our view? I don't think so because the universe is expanding faster the further you look. So for the further galaxy the speed of the far galaxy is less high than from our view because the far galaxy is further away from us. 

So is the conclusion right that the colour of the same wave is more red for us on earth than from the further galaxy?
If I understand you right, you're asking whether or not the redshift of the photons emitted from a far-away galaxy happens the instant it leaves the galaxy.

Redshift is gradual…

If so, the answer is no. The redshifting of photons happen gradually as they travel through the expanding Universe. You can find the derivation here where you'll see that every infinitesimally small increase $da$ of the scale factor $a$ of the Universe (its "size") increases the photon's redshift by an amount $dz$, or, in terms of wavelength, by an amount $d\lambda$.

If galaxy $B$ lies at redshift $z_\mathrm{B}$, then an observer in galaxy $A$ at redshift $z_\mathrm{A}$ lying between us and $B$ (so that $z_\mathrm{A}&lt;z_\mathrm{B}$) would measure $B$'s redshift to be
$$
z_\mathrm{B\,seen\,from\,A} = \frac{1+z_\mathrm{B}}{1+z_\mathrm{A}} - 1,
$$
which is less than $z_\mathrm{B}$.



…at least in our Universe

The redshifting is not due to the source moving away from us. If the expansion hadn't been gradual, but we instead lived in a crazy universe that were static when the distant galaxy emitted the light, and static when we observe, but somehow expanded suddenly by some factor in the meantime, then we would still observe a redshift, even though the galaxy were static both when it emitted the light and when we observed it.