Batch rename and copy multiple files in Windows

I have a large number of files with names like this in a same folder:

• myPic_fr.png
• myPic_it.png
• myPic_gr.png

I want to rename them to:

• myPic_fr_1080.png
• myPic_it_1080.png
• myPic_gr_1080.png

Then copy them to a new folder like this:

• ../fr/myPic_fr_1080.png
• ../it/myPic_it_1080.png
• ../gr/myPic_gr_1080.png

How to create a batch script or powershell script to do that job?

Edit: I tried this batch script code to do the rename job (Thanks @RoXX):

@echo off
setlocal EnableDelayedExpansion
SET oldPart=.png
SET newPart=_1080.png
for /f "tokens=*" %%f in ('dir /b *.png') do (
  SET newname=%%f
  SET newname=!newname:%oldPart%=%newPart%!
  move "%%f" "!newname!"
)

But for the "copy" part I don't know how to do it! Maybe need Regex?

Thanks

Sample tree before

> tree /f
    myPic_fr.png
    myPic_gr.png
    myPic_it.png

running this script:

## Q:\Test\2018\10\11\SO_52760856.ps1
Get-ChildItem *_*.png | Where-Object BaseName -match '^.*_([^_]{2})$' | 
  ForEach-Object {
    $Country=$Matches[1]
    $NewName=$_.BaseName+"_1080"+$_.Extension
    $_ | Rename-Item -NewName $NewName
    if (!(Test-Path $Country)){MD $Country|Out-Null}
    Copy-Item  $NewName (Join-Path $Country $newName)  
  }

and the tree after

> tree /f
│   myPic_fr_1080.png
│   myPic_gr_1080.png
│   myPic_it_1080.png
│
├───fr
│       myPic_fr_1080.png
│
├───gr
│       myPic_gr_1080.png
│
└───it
        myPic_it_1080.png