Open SP Management Shell (Powershell) and copy and paste:
function Sync-SPGroupEmail([string]$userName, [string]$email) {
Get-SPSite -Limit All | foreach {
$web = $_.RootWeb
if ($_.WebApplication.UseClaimsAuthentication) {
$claim = New-SPClaimsPrincipal $userName -IdentityType WindowsSamAccountName
$user = $web | Get-SPUser -Identity $claim -ErrorAction SilentlyContinue
} else {
$user = $web | Get-SPUser -Identity $userName -ErrorAction SilentlyContinue
}
if ($user -ne $null) {
$web | Set-SPUser -Identity $user -SyncFromAD
$list = $web.Lists["User Information List"]
$query = New-Object Microsoft.SharePoint.SPQuery
$query.Query = "<Where><Eq><FieldRef Name='Name' /><Value Type='Text'>$userName</Value></Eq></Where>"
foreach ($item in $list.GetItems($query)) {
$item["EMail"] = $email
$item.SystemUpdate()
}
}
$web.Dispose()
$_.Dispose()
}
}
Or can run function above from C:\Powershell\SPGroupEmail.ps1
cd \
.\Powershell\SPGroupEmail.ps1
Then put in:
Sync-SPGroupEmail "PMC1\group_name" "test@phmic.com"
This Work e-mail must be set for Alerts to be sent to AD groups from SharePoint Lists.

Reference Link