Given the Cholesky decomposition of $A$, compute efficiently Cholesky decomposition of $RAR^T$?

Question

Let $B = RAR^T$, where $A$ is positive definite and symmetric, and $R$ a generic matrix (possibly rectangular).

Suppose I know the Cholesky decomposition $A=LL^T$. Is it possible to compute the Cholesky decomposition of $B$ fast, exploiting the knowledge of $L$?

Edit: Let's assume that we also know the an LU decomposition for $R=L_RU_R$. I'm not sure if this can help to obtain the decomposition of $B$.