Cox proportional hazards model with inverse probability treatment weights: testing the Cox proportional hazards assumption

I have survival data of persons who participated/didn't participate in a health promotion program.

To estimate the effect of the health promotion program on the hazard of mortality, I plan to use a Cox proportional hazards model with inverse probability treatment weights (IPTW).

I have a query regarding the Cox proportional hazards assumption.

In testing this assumption, should inverse probability treatment weights be accounted for?

If the answer is "yes", how can I perform this testing in R?

Sorry if this question is not pertinent, I'm still learning.

Section 3.5 of "The Survival Package" vignette for the R survival package (now at version 3.2-3) discusses tests of the PH assumption. It notes that the cox.zph()function now uses a score test to examine PH rather than the approximation with a correlation test that was used in versions prior to 3.0 (and that you will probably see when you look at most on-line discussions of that function, as this change happened in late 2019; there is no longer a "rho" value reported).
The code for this new version of cox.zph() (available by typing cox.zph at the R command prompt) shows that it now looks for and incorporates case weights into its calculations, taking them from the coxph object.* The weighting is done via C code that you can inspect by downloading the source code for the package. I haven't worked through the details myself, however.
Don't just depend on the tabular output from cox.zph(). Do look carefully at the scaled Schoenfeld residual plots for each covariate against time. You might need to use your judgment, based on your knowledge of the subject matter, to determine whether a statistically significant violation of PH is also practically significant or to identify particular time periods that warrant special treatment.
*It's not clear to me whether prior versions of cox.zph()incorporated weights into the calculations, although weighted residuals needed for the test could in principle have been determined. So check the software version you are using.