Dashed hook right arrow

Add the keyword dashed. There's a simpler syntax available, which doesn't require to remember the argument positions.

Note that hook is sufficient. Similarly, two heads is simpler than twoheadrightarrow.

\documentclass[a4paper]{article}
\usepackage[T1]{fontenc}
\usepackage[utf8]{inputenc}

\usepackage{amsmath}
\usepackage{amssymb}
\usepackage{amsthm}
\usepackage{mathtools}
\usepackage{tikz-cd}

\newcommand{\Z}{\mathbb{Z}}

\begin{document}

\[
\begin{tikzcd}[row sep=huge, column sep=large]
  \Z \arrow[r,"\Phi"] \arrow[d,two heads] & R \\
  \Z_n \arrow[ru,hook,dashed,swap,"\bar{\Phi}"]
\end{tikzcd}
\]

\end{document}