Hello and welcome to Apple Support Communities, Linda!
We understand you're not seeing the archive mailbox in the Mail app. We'd be happy to provide information on how to have this appear.
Depending on the email provider, this mailbox may not be available. However, if it is, you can have it show by following these steps: Organize email in Mail on iPhone
"Organize your mail with mailboxes
In the Mailboxes list, you can view all your mailboxes, create a new one, or rename or delete one. (Some mailboxes can’t be changed.)
- Tap Mailboxes in the upper-left corner.
- Tap Edit at the top of the list.
- Select the checkboxes next to a mailbox you want to view.
- There are several smart mailboxes, such as Unread, that show emails from all your accounts. Tap the mailboxes you want to view.
- To add a mailbox, tap New Mailbox at the bottom of the list.
- Enter a name and specify a location, then tap Save."
Have a great day!