First -- I'd get him a big, kid-friendly dictionary that sits next to him all the time when he does homework. "Mom, how do I spell 'hamster'?" "What's the first letter, son? The second one? HA, you say? OK, look it up." He's going to resist and moan for a while but he needs to learn that skill. I get it --"If I can't spell it, I can't look it up in the dictionary!" But yes, he can, with some prompting from you.
So if I read this right -- he does fine on spelling tests but the issue is when he's doing other writing. Is that correct? If the teacher is going just on his spelling test scores, she may just not be aware that he has trouble with spelling the words he "should" know outside the context of a mere list on a test.
I would ask the teacher if that seems at all typical to her. I would bet there are many other kids who memorize the spelling word but can't spell the word out of the context of a spelling list -- they can hear, "Spell the word 'computer'" and they write the word that they memorized letter by letter, but when they want to write a paragraph and use the same word, they don't have a clue because it's out of the context of a simple list. Does that sound like your son?
I would tell the teacher about it in that way -- he's memorizing the "look" of the word letter by letter FOR the test and it doesn't go deeper. This sounds normal for a third grader, and after all it's still pretty early in the school year. So no need for panic or a big intervention. I would alert the teacher, now, that at home, he needs a lot more spelling help than she may see him needing in class. Make her aware of it and work with her through the year to keep an eye on it. If he doesn't improve with practice, talk to her later in the year about whether he needs any extra help.
While yes, some people are better spellers than others, please don't let him get the idea from your husband or other kids or adults that "It's OK, some people are just never good spellers." (Funny, in these STEM-intensive times, any parent would get criticized for saying, "Oh well, some people are just not good at math so it's OK not to do well at it" but it seems to be all right to dismiss spelling with "It's OK, some people are just never going to be good spellers.".....) He can learn a lot of tricks to help with spelling, and he clearly has a good memory but just needs some help expanding context.