If a person living in a foreign country, is not able to do Qurbānī, can he donate money equivalent to the price of a sheep or goat, to an Islamic organization which claims that it will perform Qurbānī on the donors behalf and distribute the meat to needy Muslims?

The answer to your question is in the affirmative. Whenever it is not possible to carry out a prescribed form of worship in its required shape and manner due to some legitimate reason, it should be done so in whatever way possible so that one is able to carry out one’s responsibility even as a token.

For example, if a person is not able to say his prayers while standing, he should do so while sitting or, even lying down if he is not even able to sit. Similarly, if carrying out ablution (wudhū) is in not possible, for a person he should do tayammum. Likewise, if one is not able to sacrifice an animal, he can do what you have proposed. This is the beauty of our religion. It does not impose undue restrictions on us nor does it compel us to carry out directives which in certain circumstances are not possible to obey