One form of Whitney embedding theorem says that if $M,N$ are smooth compact manifolds and the dimension of $N$ is more than twice the dimension of $M$, then the space of embeddings $M\to N$ is open and dense in the Whitney topology.
I need a relative version of this: if further $f: M\to N$ is such that the restriction $f|_{\partial M}$ is an embedding (as a map $\partial M\to N$), is the space of embeddings $M\to N$ that coincide with $f$ on $\partial M$ open and dense in $\{h\in C^\infty(M,N):\,\,h|_{\partial M}=f|_{\partial M}\}$?
Could you give me a reference or hint please?