Postmark will store a 1 MB copy of a message. If the message and attachment are under 1 MB, a Base64 copy of the attachment is. This is available via the "Raw Source" tab when viewing a message. For more details on size limits please see Postmark attachment limits.
Within the UI, if you scroll down in the Raw Source tab when viewing the message you can see the attachment details, including the base64. For attachments under 1 MB, the full base64 will be present and you from there you can save it to a file and then convert it back into the original file.
Attachments larger than 1 MB are truncated and not stored.