Excellent response was posted to by Bob Bills to the Finchlovers Listserv. 

A finch egg could potentially be fertilized from copulation 24 hours prior to laying. A single mating can fertilize an entire clutch. Subsequent matings may enhance the probability of fertilization. 

The avian female has the ability to store sperm in storage tubules for an extended period. I don't know exactly how long finch species can store viable sperm, but it is at least two weeks and probably longer. Larger birds (i.e. turkeys and some waterfowl species), have produced fertile eggs more than 60 days after copulation. 

Hope this is a little clearer. 

Bob Bills