You want to sign and encrypt emails with your mobile Apple device using your existing, requested S/MIME certificate.
Receiving signed and encrypted e-mails: A small check mark and, if applicable, a lock symbol appear next to the sender name for a signed and/or encrypted e-mail.
If you want to encrypt the e-mail, the error message "the recipient's certificate could not be found" appears.
This requires the installation of the certificate from the recipient beforehand. See Apple's instructions: https://support.apple.com/en-us/HT202345
Here are the individual steps:
1.) Open an email of the person,
2.) click on the name in the header,
3.) if necessary, click on the name again, then
4.) click on "Show certificate", and finally
5.) click on "Install".
For each person with whom you want to exchange encrypted e-mails, you have to repeat these steps.
Many thanks to the author Irmgard Blomenkemper from RRZK for the blog article