The "case" inbox is solved. Inbox uppercase!
I have tried all suggested syntaxes.
tell application "Mail"
set selected mailboxes of first message viewer to {mailbox "INBOX" of account "Gérard"}
-- OK if "inbox" in uppercase!
set selected mailboxes of message viewers to {inbox}
--> OK
set selected mailboxes of first message viewer to {inbox}
--> OK
set selected mailboxes of message viewers to {junk mailbox}
--> OK
set selected mailboxes of message viewers to {trash mailbox}
--> OK
set selected mailboxes of message viewers to {sent mailbox}
--> OK
set selected mailboxes of message viewers to {mailbox "Gérard" of mailbox junk mailbox}
--> No error but NO selection
set selected mailboxes of first message viewer to {mailbox junk mailbox of account "Gérard"}
--> No error but NO selection
set selected mailboxes of first message viewer to {junk mailbox of account "Gérard"}
--> No error but NO selection
set selected mailboxes of message viewers to {mailbox "Gérard" of mailbox "junk mailbox"}
--> Erreur dans Mail : Le gestionnaire AppleEvent a échoué.
--set selected mailboxes of message viewers to {mailbox "Gérard" of mailbox "INBOX"}
--> Erreur dans Mail : Le gestionnaire AppleEvent a échoué.
end tell