How to match a dataset based on a variable distribution of an other dataset?

Let say I've two datasets with similar variables but different distribution. In the example below, dataset a has a variable var1 with a mean of 10 and a sd of 4. Dataset b has also variable var1 but with a mean of 8 and a sd of 4.

a <- data.frame(id=1:500,var1=rnorm(500,10,4),type="a")

b <- data.frame(id=1:300,var1=rnorm(300,8,4),type="b")

rbind(a,b) %>%
  ggplot(aes(x=type,y=var1)) +
  geom_boxplot()

Is there a way to filter dataset b to match dataset a's var1 distribution ? When I say match, mean and sd should be similar (not necessarly equal)

I tried using MatchIt package to match a and b dataset but it filters also some entries from dataset a.

Any idea ?

Thanks

Edit>

Here's the real shape of a and b density (from my data). a is red, b is blue