Advice on when to purchase the full JR Pass

Hello, we will be arriving in Tokyo on the 31st July from the UK, and hopefully will exchange the voucher for the JR Pass on that date, jet lag willing!

Can you please advise on when I should make the JR Pass purchase order so that it arrives in plenty time at my home in the UK (but within the three month exchange deadline) - ie. should i purchase in May? I just want to be double sure I don't mess up.

Many thanks for your help. Priya