Congratulations on the receipt of your cards.
If you're planning on moving at the end of May, you might want to wait until then, unless you already know the address of where you'll be moving to before initiating the GC replacement process - you'll need to provide an address for this.
You'll need to cross check all the forms you submitted to confirm you guys did not mix up the DOB during your applica process. If the error is solely from USCIS, you're eligible for a free replacement. All you'll have to do is fill out the applicable form, include the GC and send back the package to USCIS.
If it turns out you guys did mix up the dates on your form(s), then you'll have to pay for the replacement which is about $450 now, if I'm not mistaken.
The replacement process could take up to 6 months (or longer), so you'll need to exercise lots of patience.