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Yes, you can invite anyone to visit. But even if you were a U.S. Citizen inviting, that isn't what the U.S. government cares about. What they want to see is that the person has strong ties to their home that they will not abandon and that they will go home after their visit.
You can look at the link below for all the information that you need:
Essentially, the person must have a valid reason for visiting, must have a way to support themselves without working illegally, must have significant ties to their home country, and must have the intent to return home.
A letter of invitation helps with some of this as it will help to show why the person is coming to the U.S., how much time they will need and that perhaps they will have a place to stay so they don't have to spend money. Usually you want to show that the person is going just for a few weeks or so. If it is longer than that, immigration will wonder why and will become suspicious. They are almost sure to deny someone that says they want to visit for 5 or 6 months unless they have very strong evidences of everything else I listed above. But keep in mind that a letter of invitation is a small part of the process and isn't even a requirement (people mistakenly believe it is the most important) and it can sometimes be used against the applicant. For example, if the consular officer believes that the applicant will have too much support meaning that they could stay illegally in the U.S. or if there is a romantic connection, the officer would deny the visa. Sometimes it is better to not even have a letter of invitation. The most important part of a case is to have strong ties to the home country.
So a letter of invitation should state why you are inviting them and that you will provide room and board while they are here visiting.
Now as to some of the ties, they will need to show that they have significant close family at home, property not easily sold, and a good job for a good company that they have had for awhile that a person would not normally abandon.
So if the person is young, without much money or any property, they could be denied. They would be a risk for staying illegal. Also, persons that are planning to travel with their spouse and children are a risk as well because some of their significant ties are actually going with them.
I mean some people have been approved with less, but I am trying to give you the idea for the best chance.
So yes, you can invite, but the invitation doesn't really mean as much as you may think.
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