Draw arrows between nodes defined in a pic

Question

How can I draw an arrow between two nodes that are defined in a pic please. For example, how can I draw an edge from node A in the left hand side to the node A in the right hand side? Thank you.

My code:

\documentclass[border=10pt]{standalone}    
\usepackage{tikz}
\usetikzlibrary{arrows, calc}
\begin{document}
\tikzset{
arrow/.style={draw, -latex},
mypic/.pic = {  
  \node[draw] (a) {A};
  \node[draw, below of=a] (b) {B};}
}
\begin{tikzpicture}
  \pic at (0,0) {mypic};
  \pic at (1,1) {mypic}; 
  \draw[arrow] (a.north east)--(a.south west); % unsurprisingly this doesn't work
\end{tikzpicture}
\end{document}

Answer 1

You overwrite the node a. You need to give it unique names, e.g. with.

\documentclass[border=10pt]{standalone}    
\usepackage{tikz}
\usetikzlibrary{arrows, calc}
\begin{document}
\tikzset{
arrow/.style={draw, -latex},
mypic/.pic = {  
  \node[draw] (#1-a) {A};
  \node[draw, below of=#1-a] (#1-b) {B};}
}
\begin{tikzpicture}
  \path (0,0) pic {mypic=L};
  \path (1,1) pic {mypic=R}; 
  \draw[arrow] (L-a.north east)--(R-a.south west); 
\end{tikzpicture}
\end{document}

In principle you could also use the names of the pics, see the example on top of p. 263 of the pgf manual. However, in practice difficulties arise, so I decided to go the way above.