package bcmwl-kernel-source (not installed) failed to install/upgrade: subprocess installed post-installation script returned error exit status 3

[John Shakespeare]

On upgrading a Dell M4400 from Trusty 14.04.3 to Xenial 16.04.1, the Broadcom wireless (which had been working in Trusty) failed to load. It's a Broadcom 14e4:432b according to lspci.

On installing Xenial in another partition, the Broadcom wireless worked flawlessly. I would rather not revise all of my settings to this partition, as there is a _very_ large number of them.

ProblemType: Package
DistroRelease: Ubuntu 16.04
Package: bcmwl-kernel-source (not installed)
ProcVersionSignature: Ubuntu 4.4.0-36.55-generic 4.4.16
Uname: Linux 4.4.0-36-generic x86_64
NonfreeKernelModules: wl
ApportVersion: 2.20.1-0ubuntu2.1
AptOrdering:
 bcmwl-kernel-source: Install
 bcmwl-kernel-source: Configure
 NULL: ConfigurePending
Architecture: amd64
Date: Thu Aug 18 22:38:28 2016
ErrorMessage: subprocess installed post-installation script returned error exit status 3
InstallationDate: Installed on 2014-10-03 (684 days ago)
InstallationMedia: Xubuntu 14.04.1 LTS "Trusty Tahr" - Release amd64 (20140723)
RelatedPackageVersions:
 dpkg 1.18.4ubuntu1.1
 apt 1.2.12~ubuntu16.04.1
SourcePackage: bcmwl
Title: package bcmwl-kernel-source (not installed) failed to install/upgrade: subprocess installed post-installation script returned error exit status 3
UpgradeStatus: Upgraded to xenial on 2016-08-01 (17 days ago)