You are using the Document ID Service in SharePoint and you want to move your documents to another location.  For whatever reason, you notice when you move the documents that your document id’s are lost or reset.  This can be real bad if other systems outside of SharePoint leverage the document id to locate documents in SharePoint.

Here are the steps I used to get around this.
Move the documents from location A to B, keeping the original documents in A.
Run a crawl.
Execute the script below (input your own values for the site and libraries).
Remove / delete the documents from location A. For safe measures, also empty the recycle bin, both at the site and site collection level.
Run another crawl.
Trigger the Document Id Settings to update.

What the script is doing:
Get all the documents in the Shared Documents library of site A.
Loop through the documents.
Locate the document by name in the Shared Documents library of site B.
Update the Document ID of the item.

Things you could improve on:
Get all the documents in site A and output the Name and Document ID to a csv file.
– Then process the csv file with the script.
Add logging.
– Output your pass / fail items to csv file.
Expand the search to query a site.
– Then update the returned item.

if ((Get-PSSnapin "Microsoft.SharePoint.PowerShell" -ErrorAction SilentlyContinue) -eq $null)
{
    Add-PSSnapin "Microsoft.SharePoint.PowerShell"
}

$sSite = Get-SPWeb "http://sharepoint.net/sites/A"
$sList = $sSite.lists["Shared Documents"]

$dSite = Get-SPWeb "http://sharepoint.net/sites/B"
$dList = $dSite.lists["Shared Documents"]

$sQuery = New-Object Microsoft.SharePoint.SPQuery
$sQuery.ViewAttributes = "Scope='Recursive'"
$sQuery.RowLimit = 2000
$sQuery.Query = '<Where><Gt><FieldRef Name="ID" /><Value Type="Counter">0</Value></Gt></Where>'

do
{
	$sItems = $sList.GetItems($sQuery)
	$sQuery.ListItemCollectionPosition = $sItems.ListItemCollectionPosition
	foreach($sI in $sItems)
	{
		$docName = $sI["Name"].ToString()
		Write-Host $docName

		$dQuery = New-Object Microsoft.SharePoint.SPQuery
		$dQuery.ViewAttributes = "Scope='Recursive'"
		$dQuery.RowLimit = 2000
		$dQuery.Query = '<Where><Eq><FieldRef Name="FileLeafRef"/><Value Type="File">' + $docName + '</Value></Eq></Where>'

		do
		{
			$dItems = $dList.GetItems($dQuery)
			$dQuery.ListItemCollectionPosition = $dItems.ListItemCollectionPosition
			foreach($dI in $dItems)
			{
				try
				{
					$dI["Document ID Value"] = $sI["Document ID Value"]
					$dI.Update()
					Write-Host $dI["Name"] " has been updated"
				}
				catch
				{
					Write-Host $dI["Name"] " ---- " $_.Exception.Message
				}
			}
		}
		while ($dQuery.ListItemCollectionPosition -ne $null)
	}
}
while ($sQuery.ListItemCollectionPosition -ne $null)