SQL Server Link foreign key on join using each row on the right table only once - sql-server

Question

I have two tables
CREATE TABLE remote_clients (
id INT NOT NULL IDENTITY PRIMARY KEY
first_name VARCHAR(255),
last_name VARCHAR(255),
date_of_birth DATE
)
and
CREATE TABLE local_clients (
id INT NOT NULL IDENTITY PRIMARY KEY
first_name VARCHAR(255),
last_name VARCHAR(255),
date_of_birth DATE,
remote_client_id INT FOREIGN KEY REFERENCES remote_clients(id)
)
I want to link all the local_clients with a row from remote_client with matching name and date of birth, but each remote_client can only be linked with one local_client.
How can I do this in one update query?
Examples
INSERT INTO local_clients
(first_name, last_name, date_of_birth)
VALUES
('foo', 'bar', '2020-01-01'),
('foo', 'bar', '2020-01-01'),
('baz', 'lurman', '2020-01-01'),
('steve', 'last', '2020-01-01'),
('steve', 'last', '2020-01-01'),
('aaron', 'something', '2020-01-01')
INSERT INTO remote_clients
(first_name, last_name, date_of_birth)
VALUES
('foo', 'bar', '2020-01-01'),
('foo', 'bar', '2020-01-01'),
('baz', 'lurman', '2020-01-01'),
('baz', 'lurman', '2020-01-01'),
('steve', 'last', '2020-01-01'),
After the update, my local_clients should look like this
id
first_name
last_name
date_of_birth
remote_client_id
1
foo
bar
2020-01-01
1
2
foo
bar
2020-01-01
2
3
baz
lurman
2020-01-01
3
4
aaron
something
2020-01-01
NULL
5
steve
last
2020-01-01
5
6
steve
last
2020-01-01
NULL

Answer 1

UPDATE local_clients
SET remote_client_id = subQuery.id
FROM local_clients
INNER JOIN (
SELECT
local.id,
remote.id,
---Get the row number, paritioned by the local ID so it's only joined once
ROW_NUMBER() OVER(PARTITION BY local.id ORDER BY local.id) AS row_number
FROM local_clients AS local
INNER JOIN remote_clients AS remote ON
local.first_name = remote.first_name AND
local.last_name = remote.last_name AND
local.date_of_birth = remote.date_of_birth
WHERE NOT EXISTS ( ---The remote client isn't already linked
SELECT remote_client_id
FROM local_clients
WHERE local_clients.remote_client_id = remote_clients.id
)
) AS subQuery
WHERE NOT EXISTS ( ---The local client isn't already linked
SELECT * FROM remote_clients WHERE local_clients.remote_client_id = remote_clients.id
)
--- If there are multiple remotes, only get the first
AND subQuery.row_number = 1