  Strong gravitational lensing effect is a powerful tool to probe cosmological
models and gravity theories. Recently, the time-delay cosmography from strong
lensing and the stellar kinematics of the deflector, which encode the Hubble
constant and the post-Newtonian parameter via two distance ratios reflecting
the lensing mass and dynamical mass respectively, have been proposed to
investigate these two parameters simultaneously. Among strong lensing systems
with different sources, strongly lensed fast radio bursts (FRBs) have been
proposed as precision probes of the universe since the time delay $\sim$ 10
days between images could be measured extremely precisely because of their
short duration of a few milliseconds. In this work, we investigate the ability
of strongly lensed FRBs on simultaneously estimating these two parameters via
simulations. Take the expected FRB detection rate of upcoming facilities and
lensing probability into consideration, it is likely to accumulate 10 lensed
FRBs in several years and we find that $H_0$ could be determined to a
$\sim1.5\%$ precision and $\gamma_{\rm PPN}$ could be constrained to a
$\sim8.7\%$ precision simultaneously from them. These simultaneous estimations
will be helpful for properly reflecting the possible correlation between these
two fundamental parameters.
