I posted a long reply to your message, but just as I hit "post message" my connection was lost and so was my message.I'm only now getting back to it.
Your points are all well-taken.I didn't include much of the information I had about "my" Axel Vallin in my post.He was married in Chicago in 1900.According to information he gave to the censuses, he immigrated in 1893 and was born about 1871-1872.This information, combined with the marriage of a Hilma C Wallin in Chicago in the same period suggested that "my" Axel might have been identical to the Axel in the family you referred to (from Mjolby).
I traced that Axel (from Mjolby) forward through in- and ut-flytting and church records and determined that he was the Axel Wallin/Vallin who emigrated from Viby in 1894 (and appears on your list twice under these two spellings).This Axel listed his destination as Chicago, emigrated in 1894 and was born in 1869.This made him not a bad fit for "my" Axel, but not a definite identification because of the small discrepencies in dates (which are not unusual in census info, but were still sufficient to make the identification uncertain).
From the emigrant list you posted, there are several other possibilities that I should examine more in detail to see if I can trace them on the U.S. end (and thus show whether they are definitely NOT "my" Axel).
I would also like to have an exact date of birth in order to confirm the identity whenever I find it.I do not, however, have this information right now.
I posted my original message in hopes of finding out more about this document of inheritance that was mentioned in the post to which I was responding.If the woman in Sweden mentioned her daughter Hilma, it seems that she might also have mentioned other children (if she had them).Knowing what she said might be helpful in identifying other immigrants in the family (since, as I mentioned, I know that the Axel in this particular Mjolby family emigrated to America in 1894).
Thanks a lot for the very informative post, and I will certainly be taking your advice to heart before deciding I have found the origins of "my" Axel.