Searching a Wallet Item (Membership) does not find the field Membership #,
even if "Include notes and password in search (slower)" is checked.
If I copy the Membership # in the field note, the search is working as espected,
That's correct. The option is to "include notes and passwords…" not memberships numbers, but I'll create a feature request if you would like. One question, though: if you already know the membership number why are you searching for it? Just curious.