The link you provided above is in Midtown Manhattan area, not in Brooklyn. Is this the apartment you are referring to or did you mean to post another link?
Wherever it may be, Brooklyn or Manhattan it doesn't matter for the conversation sake.
You have to find out if your client has a bank account in United States, if she doesn't there is a good chance that she may need to set something up here before she considers making a real estate purchase.
Setting up an account shouldn't be too complicated. She should check if her current bank in Belgium has any branches here in New York. If they do, it will be a smooth transition. I know that HSBC is more known in Europe then here in US, although it's a major bank here as well. And if she happens to bank with HSBC they can easily open an account and verify all of her financial information.
I recently helped one of my clients set up a personal and a business account with HSBC, she's a foreign national. It doesn't have to be this bank, it can be any, I'm only bringing it up because I worked with them and they took care of everything.
The link for the property you posted is a Co-op. I'm not sure if Belgium has Co-ops, you may only have homes and condos. The difference is that in a Co-op you a own a % of shares in the building which you share with your neighbors and in a Condo you own the real property. Co-ops have co-op boards which consist of members of the building who interview every potential buyer in the building and who have the right to turn people away, and not always for a reason they will ever say.
I'm not sure how long your client is planning on living in New York, if she want's to be a permanent resident, she can very well consider a coop. If on the other hand she is going to be using this as an investment, then in that case she probably wont be able to purchase in a Coop building and will have to look at Condos only.
Coops don't like investors, the members in the building want to know who the neighbors are and prefer not having a revolving door of residents.
Also in a coop after the typical closing costs, they require higher income restrictions and they require liquid cash in the bank after all the other closing costs in case that buyer defaults. Basically they want to make sure that if you buy here, and you lose your job you can still afford to pay for the apartment.
Typial closing costs for a condo:
Attorney - between $1000-$2500
Bank Fee $ 750
Processing fee $ 330
Appraisal fee $300-$1,500 (depends on the sale price)
Credit report fee $10-30
Bank Attorney $ 650
Tax escrows 2 to 6 months
Recording fee $250-750
Mortgage Tax 0.8%
Fee tittle insurance approx $450 per $100000 of sale price under 1M
Mortgage title insurance approx $130 per $100000
Municipal Search $350-$500
Mansion Tax 1% of entire purchase if over $1Million
NYC mortgage tax A. mortgage less than $500,000 is 1.80%
over $500,000 2.80%
Those are the typical fees your client will have to inquire.
Hope this helps answer your question.
If you have any others, please don't hesitate to email me or call me. All of my contact information is in my profile.