Ruling on making up fasts on behalf of a deceased person who did not fast, with or without an excuse
Question

                My father died when I was small, but the problem is that my mother shocked us one day by telling us that she never saw my father fasting in Ramadaan from the beginning of their marriage until he died (approximately 11 or 12 years), and that she did not know whether he fasted before their marriage, because my father worked as a truck driver 

My question is, how can we make up for these years on my father’s behalf, when we do not know how many they were, or anything about his fasting during his life which lasted for 60 years?

There is also a question from my mother: during the years when she first reached puberty, before she got married, she did not fast because she was unaware of the importance of fasting, as she was living in the desert. She became religiously committed from the time of her marriage, but she does not remember how many days she missed. That was 36 years ago; how should she make up those days?.
Praise be to Allah.
    Firstly: 

    If a person does not fast because of an excuse such as travel 
    or sickness from which he hopes to recover, then he has to make it up. If he 
    dies without making it up, even though he was able to do so, then it remains 
    an obligation that must be fulfilled, and it is mustahabb for his 
    next-of-kin to fast on his behalf, because of the hadeeth of ‘Aa’ishah (may 
    Allah be pleased with her), according to which the Messenger of Allah 
    (blessings and peace of Allah be upon him) said: “Whoever dies owing any 
    (obligatory) fasts, his next-of-kin may make them up on his behalf.”

    Narrated by al-Bukhaari, (1952), Muslim (1147). 

    But if he dies before he is able to make them up, such as one 
    whose illness lasts until he dies, then he does not have to do anything and 
    his next-of-kin do not have to do anything on his behalf. 

    If a person does not fast out of carelessness and 
    heedlessness, and has no excuse, he does not have to make them up and they 
    are not valid if he does, because the time for them has ended. 

    This has been discussed previously in the answer to question 
    no. 50067 and
    81030 

    Based on that: 

    What appears to be the case with your father, as he was keen 
    to pray and do good, is that he would not have refrained from fasting 
    without an excuse, so it seems that he refrained from fasting because of the 
    excuse of travel, and it is not known whether he made up those days whilst 
    travelling or in the winter, for example -- and your mother does not know 
    either -- or whether he did not make them up. Was it possible for him to 
    make them up when he had a break from work and stayed home, or was he always 
    travelling because of the nature of his work, so that he was not able to 
    make up what he had missed until he died? 

    In the face of these possibilities, we say: if you cannot 
    find out the facts of the matter, and you fast on his behalf as much as you 
    are able to, this is a good and righteous deed for which you will be 
    rewarded in sha Allah. But it is not obligatory and you do not have to find 
    out the exact number of years he did not fast; rather you should act upon 
    what is most likely to be the case and decide on the number of years that he 
    did not fast, then fast on his behalf as much as you can. This comes under 
    the heading of ihsaan (kind deeds), but it should not distract you from 
    other deeds that are more important and more beneficial. 

    It is permissible for all the heirs to join in this making up 
    of fasts. Whatever it is too hard for them to fast, they may feed poor 
    persons instead, one poor person for each day. 

    Shaykh Ibn ‘Uthaymeen (may Allah have mercy on him) said: It 
    is mustahabb for his next-of-kin to make it up if he did not do it. We say: 
    for each day, feed one poor person. 

    And he said: If we assume that a man has fifteen sons, and 
    each of them wants to fast two days to make up for thirty days, that is 
    acceptable. If there were thirty heirs and they all fasted one day each, 
    that would be acceptable, because they fasted thirty days between them. It 
    makes no difference whether they all fast on the same day or one of them 
    fasts one day, then the next fasts the next day, and so on until they 
    complete thirty days.

    End quote from ash-Sharh al-Mumti‘, 6/450-452 

    Secondly: 

    With regard to the fasts your mother did not observe from 
    after she reached puberty and until her marriage, this matter is subject to 
    further discussion, as follows: 

    1-Whatever she did not do out of 
    heedlessness and carelessness, with no excuse, she does not have to make up, 
    as stated above.

    2-Whatever she did not do because 
    of an excuse such as menses, travel or sickness, she has to make up. She 
    should try hard to work out the number of days or what she thinks is most 
    likely.

    And Allah knows best.