Simulating copula with copula::normalCopula: what is the covariance of output?

Question

I am trying to simulate data from a normal Copula using R's copula package, more precisely using normalCopula and then mvdc. I note that the function normalCopula wants the correlation matrix R, not the covariance S. Looking at the output, I note that while the cor of the sample is close to the population R, the cov of the simulated data is not close to my population S, even when rescaling by the S' variances?

So: what is the covariance of the output of mvdc(copula=normalCopula(param=P2p(cov2cor(SIG)),...), if it is neither R nor (rescaled) S? I suspect the output covariance is a mix of the input correlation R and the marginal variances/moments? How should I rescale my data so that it has covariance S?

library(copula)
S <- matrix(c(0.5, 0.8, 0.7, 0.8, 2, 0.2, 0.7, 0.2, 8), 3,3)
R <- cov2cor(S)

## Simulate data with cpula package
myCop <- normalCopula(param=P2p(R), dim = 3, dispstr = "un")
myMvd <- mvdc(copula=myCop, margins="gamma",
              marginsIdentical=TRUE,
              paramMargins=list(list(shape=2, scale=1)))
X_copula <- rMvdc(5000000, myMvd)

## check resulting cov?
cor(X_copula);R # yes, they seem to be close
#>           [,1]       [,2]       [,3]
#> [1,] 1.0000000 0.78346901 0.32660893
#> [2,] 0.7834690 1.00000000 0.04496475
#> [3,] 0.3266089 0.04496475 1.00000000
#>      [,1] [,2] [,3]
#> [1,] 1.00 0.80 0.35
#> [2,] 0.80 1.00 0.05
#> [3,] 0.35 0.05 1.00
X_copula_rescale <- X_copula%*% diag(sqrt(diag(S))) # rescale by vaariance
cov(X_copula_rescale);S # far!?
#>          [,1]      [,2]       [,3]
#> [1,] 0.999889 1.5666511  1.3075266
#> [2,] 1.566651 3.9989791  0.3599924
#> [3,] 1.307527 0.3599924 16.0285098
#>      [,1] [,2] [,3]
#> [1,]  0.5  0.8  0.7
#> [2,]  0.8  2.0  0.2
#> [3,]  0.7  0.2  8.0
cov(X_copula_rescale)/2;S
#>           [,1]      [,2]      [,3]
#> [1,] 0.4999445 0.7833255 0.6537633
#> [2,] 0.7833255 1.9994895 0.1799962
#> [3,] 0.6537633 0.1799962 8.0142549
#>      [,1] [,2] [,3]
#> [1,]  0.5  0.8  0.7
#> [2,]  0.8  2.0  0.2
#> [3,]  0.7  0.2  8.0

^{Created on 2023-03-13 with reprex v2.0.2}