No, the Committee has NOT issued any formal letter of invitation, but only validated your application by simple mail during the last months (mail subjects: Confirmation for Assisi 2022 / The Economy of Francesco event 2022 – Reply): that is enough and you can proceed through official registration on the Participants Area.
In case you need the letter for VISA matters please ask for it by email to visa@francescoeconomy.org, or for other specific issues linked to work and study permission ask for it to community@francescoeconomy.org.