Does a strong acid's conjugate base act as Brønsted-Lowry base?
In theory, a Brønsted-Lowry base is a chemical substance which can accept a proton.

But in the case of a strong acid, the acid will lose a proton and form a weak conjugate base. Say there is a strong acid HA.

$$\ce{HA + H2O &lt;=&gt; A- +H3O+}$$

So if we take a certain quantity of HA, most of it will undergo the forward reaction since HA is a strong acid. A- is a weak base and will not want to accept the proton and thus only a small quantity of the conjugate base will do undergo the backward reaction. Hence practically, you could say that the conjugate base of a strong acid is not a Brønsted-Lowry base because of its reluctancy to accept the proton.