Creating a hardlink to a file

I'm trying to relink a file someone tried to delete while a process (that we don't want to shutdown) also had a filehandle open to it.
Consequently, we've got an inode entry but no directory entry (aka 'file') for it.

I've tracked the inode number down via lsof, as well as the particular filehandle the process has within the /proc filesystem.

This filehandle is presented as a standard "file"/directory entry in /proc/<pid>/fd and I can read from it ok as I would any other file.

I was hoping to create a link to it back where it used to be but I keep getting a 'No such file or directory' error. I know I've got my ln syntax correct as I've tested it out on plain files elsewhere.

ln /proc/<pid>/fd/<handle> /path/to/application/logs/access

Is ln the tool to use here? Surely if I know the inode number, filehandle and what it used to be called, I can recreate it?