Prayer and fasting of a prisoner who does not know anything about time

Firstly:

We ask Allaah to grant all Muslim prisoners a rapid release,
and to grant them patience and consolation by His bounty, and to fill their
hearts with peace and certainty of faith, and to make easy for the Muslims a
way of guidance whereby His close friends will be honoured and His enemies
will be humiliated. 

Secondly: 

The scholars have determined that prayer and fasting are not
waived for prisoners and detainees, and that what they must do is to try
their best to work out the right times. If the prisoner thinks it most
likely that the time for prayer has come, then he should pray, and if he
thinks it most likely that Ramadaan has come, then he should fast. He can
work out the times by noting the times when he is fed, or by asking the
guards and so on. 

If he tries to work out the right time for praying and
fasting, then his worship will be valid and acceptable, whether he finds out
later on that he did it at the right time, or after it, or he does not find
out anything, because Allaah says (interpretation of the meaning): 

“Allaah burdens not a person beyond his scope”

[al-Baqarah 2:286]

“Allaah puts no burden on any person beyond what He has
given him”

[al-Talaaq 65:7]

But if he finds out that he fasted on the days of Eid, he
should make them up, because fasting on the days of Eid is not valid. 

But if he finds out later on that that he prayed or fasted
before the proper time, then he has to repeat the fast or prayer. 

It says in al-Mawsoo’ah al-Fiqhiyyah (28/84-85): 

The majority of fuqaha’ are of the view that if the months
all seem to be the same to a person, the fast of Ramadaan is not waived in
his case, rather it is still obligatory because he remains accountable and
the ruling still applies to him.  

If he tries to work it out and he fasts, then one of the
following five scenarios must apply to him: 

1 – The problem continues and he cannot find out, so he does
not know whether he managed to fast at the time of Ramadaan or before it or
after it. In this case his fast is valid and he does not have to repeat it,
because he did his best, and he is not required to do any more than that. 

2 – The fast of the prisoner coincided with Ramadaan, so that
is acceptable. 

3 – If his fast happened to be after Ramadaan, that is also
acceptable according to the majority of fuqaha’. 

4 – There are two possibilities with the fourth scenario: 

(i)If he started fasting before
Ramadaan, and he finds out about that before Ramadaan comes, then he must
fast when Ramadaan comes, and there is no difference of opinion among the
scholars concerning that.

(ii)If he started fasting before
Ramadaan and he did not find out about that until after it had finished.
There are two opinions as to whether this is acceptable:

(a)It is not acceptable for
Ramadaan, rather he has to make it up. This is the view of the Maalikis and
Hanbalis.

(b)It is acceptable as Ramadaan,
just as if the pilgrims are uncertain of the day of ‘Arafah and they observe
the standing before the day. This is the view of some of the Shaafa’is.

5 – If the fast of the prisoner coincides with one part of
Ramadaan and not the other; that which coincides with Ramadaan or comes
after it is acceptable, and that which comes before it is not acceptable.
End quote. 

See: al-Majmoo’ (3/72-73) and al-Mughni (3/96) 

And Allaah knows best.