You can view all the members this way:
https://video2.skills-academy.com/en-us/exchange/recipients/dynamic-distribution-groups/view-dynamic-distribution-group-members?view=exchserver-2019
Example:
$group = "Full Time Employees"
Get-Recipient -RecipientPreviewFilter (Get-DynamicDistributionGroup $group).RecipientFilter
Now that you have the group - you can output the SAMAccountName
$Users = (Get-Recipient -RecipientPreviewFilter (Get-DynamicDistributionGroup $group).RecipientFilter).SamAccountName
$users should show all the SAMAccountNames of the group members Use that to add to the new group ( I am assuming this is an on-prem AD group)
Use: Add-ADGroupMember
$users | % {Add-ADGroupMember -identity SecurityGroup -members $_ }