In order to bring his daughter to the UK, he will have to satisfy the requirements of rule 297 of the Immigration rules. Under Rule 297(i) there are different options under which you can apply depending on which suits your circumstances the best.
(a) both parents are present and settled in the United Kingdom; or
(b) both parents are being admitted on the same occasion for settlement; or
(c) one parent is present and settled in the United Kingdom and the other is being admitted on the same occasion for settlement; or
(d) one parent is present and settled in the United Kingdom or being admitted on the same occasion for settlement and the other parent is dead; or
(e) one parent is present and settled in the United Kingdom or being admitted on the same occasion for settlement and has had sole responsibility for the child's upbringing; or
(f) one parent or a relative is present and settled in the United Kingdom or being admitted on the same occasion for settlement and there are serious and compelling family or other considerations which make exclusion of the child undesirable and suitable arrangements have been made for the child's care;
Both of the child's parents are still living, though separated which rules out (a)-(d) and it is unlikely that your husband will be able to demonstrate that he has sole responsibility since the child has been living with her mother who has presumably been making the day to day and major decisions in her life, even if it is funded by your husband.
The most likely category is therefore (f). You would need to provide evidence of the mother's illness, if possible, medical evidence that she is no longer well enough to care for the child, consent from the mother that the child can be looked after by your husband and if possible, a court order granting custody to your husband.
Other than the above, you husband would need to show that he can afford to maintain and accommodate her without recourse to additional public funds and that she is under 18 and not living and independent life or married.
You will need to apply to the Jamaican Embassy on form VAF4A and the fee is currently £750 but will be going up to £810 on 6 April 2011. The form can be completed online and payment made in local currency. All supporting documents will then need to be forwarded to the Embassy for consideration. Details can be found here http://www.ukvisas.gov.uk/en/applyonline/
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