It basically depends on when there is a free date on your parish’'s calendar. I was lucky. When my father passed away in 2008, I arranged 2 Masses for him within a couple of weeks of his passing.
Just to make sure, the official meaning of a Memorial Mass is just like a Mass of Christian Burial (aka Funeral Mass) without the body or cremains present. If you wish to arrange this, speak to your parish office.
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