Why can't I install PSReadLine - powershell

Question

I am trying to install the PSReadLine module:
PS> Find-Module PSReadLine | Install-Module -scope currentUser -force
This command runs and terminates without any message or any indication that something was unsuccessful.
However, when I want to load the module, I get an error message:
PS> import-module PSReadLine
import-module : The specified module 'PSReadLine' was not loaded
because no valid module file was found in any module directory.
So, I am wondering how I can install and/or load this module.
Feedback on comments
As per #Lee_Dailey's comment, I do indeed have a path with a lowercase l:
PS> ls 'C:\Program Files\WindowsPowerShell\Modules\psread*' -name
PSReadline
Unfortunately, I cannot change that lowercase l to a L because I have this issue on a machine without admin privileges.
As per #Scepticalist comment, I should find the module in one of the module paths' locations. It turns out: I don't. The following command returns/prints nothing:
foreach ($mp in $Env:PSModulePath -split ';') { ls "$mp\psread*" }
Thus, also the command suggested by #pwnosh returns nothing:
($env:PSModulePath -split ';' | Get-ChildItem -Filter 'PSReadLine' | Get-ChildItem).FullName
Find-Module PSReadLine returns (echoes)
Version Name Repository Description
------- ---- ---------- -----------
2.1.0 PSReadLine PSGallery Great command line editing in the PowerShell console host
Running Register-PSRepository -Default results in an error message:
PackageManagement\Register-PackageSource : Module Repository 'PSGallery' exists.
Set-PSRepository 'PSGallery' -InstallationPolicy Trusted runs and terminates without any message echoed to the console. Yet, after running this command, I am still unable to import the module.