Probably not. Generally, from year to year, the influenza virus mutates to create one or more new strains. (It has to do with the naked RNA or DNA which can be more easily made to mutate than the DNA in your cells, which is pretty well-protected inside a nucleus. I'm not sure whether the inflenza virus has DNA or RNA, nor if it has perhaps a small protein coat over the DNA/RNA. It's been a long time since I studied biology.) They usually are different enough that the immune system of someone who had the last strain of flu wont recognize the new one as flu, and their antiquated antibodies won't be effective against the new strain.
This is why you have to get a flu shot every year; last year's usually won't help much.