Is allowed for us Muslim to pratice artificial insemination in producing aminal. (like upgrading of a native goat to hibreed one)

All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad, sallallaahu ‘alayhi wa sallam, is His slave and Messenger.

There is no religious prohibition for using artificial insemination or what is called genetic engineering in plants and animal’s eugenics, provided this does not lead to any harm.

The Islamic Fiqh (Jurisprudence) Committee in its fifth conference passed a resolution about genetic engineering. The sixth article of this resolution reads, "It is permissible to use the instruments of genetic engineering and its means in animal reproduction and breeding, on the condition of taking all precautions in order to prevent any harm on the person, animal or environment  - even if that (harm) would be in the long run.”

After mentioning the situations where it is possible to use genetic engineering, one researcher clarified that it is a condition that this method should be safe from any change which may cause misuse or lead to anything which is of no benefit, like making wings of an eagle for a hen, or making some limbs for some animals which originally did not have these limbs; He said, "Such alterations and changes neither lead to any benefit nor repel any harm, rather they simply lead to the loss of money and effort.”

Finally, it should be noted that Islam encourages acquiring knowledge and benefiting from the universal laws set by Allaah for His creation in a way which achieves benefit or repels harm, and provided it does not contract Allaah's laws.

Allaah Knows best.