There's 2 ways to connect to office365 through powershell.

MSOL

Exchange online.

You can add members to a security group using MSOL but you have to use EOL for distribution groups or mail-enabled security groups.

At this juncture I only know how to get user data using msol.

(we use -like @ domain because pupils have a different subdomain)

#connect MSOL
connect-msolservice

get-msoluser -all | where-object {$_.userprincipalname -like  "domain"} | export-csv -path "d:\staffemails.csv" 

#connect EOL
$UserCredential = Get-Credential
$Session = New-PSSession -ConfigurationName Microsoft.Exchange -ConnectionUri [url]https://outlook.office365.com/powershell-liveid/[/url] -Credential $UserCredential -Authentication Basic -AllowRedirection
Import-PSSession $Session -DisableNameChecking

import-csv "d:\staffemails.csv" | foreach {add-distributiongroupmember -identity "groupname" -member $_.userprincipalname}