Cascade update sql trigger - sql

Question

I have two tables in two different databases Lab15DB_1 and Lab15DB_2.
The parent table is Author and the child table is Book.
Here they are:
CREATE TABLE Author
(
AuthorId INT NOT NULL PRIMARY KEY,
AuthorName NVARCHAR(50) NOT NULL,
AuthorSurname NVARCHAR(50) NOT NULL,
)
CREATE TABLE Book
(
BookId INT NOT NULL PRIMARY KEY,
BookName NVARCHAR(50) NOT NULL,
BookType NVARCHAR(50) NOT NULL CHECK(BookType IN ('Science', 'Hobby', 'Cooking', 'Fishing', 'Nature', 'Favorites')),
PublishYear INT NOT NULL,
AuthorId INT NOT NULL,
Price MONEY CHECK (PRICE > 0.0)
)
I want to create cascade update via triggers.
Here is an attempt to create trigger for cascade update on the Author table:
CREATE TRIGGER UpdateAuthorTrigger
ON Author
FOR UPDATE
AS
DECLARE #intRowCount int
SELECT #intRowCount = ##ROWCOUNT
IF #intRowCount > 1
BEGIN
IF UPDATE(AuthorId)
BEGIN
UPDATE Author
SET AuthorId = AuthorId
/* some code for update Book*/
END
END
ELSE
IF #intRowCount = 1
BEGIN
IF UPDATE(AuthorId)
BEGIN
UPDATE Author
SET Author.AuthorId = (SELECT AuthorId FROM INSERTED)
FROM Author
INNER JOIN DELETED ON Author.AuthorId = DELETED.AuthorId
UPDATE Lab15DB_1.dbo.Book
SET Lab15DB_1.dbo.Book.AuthorId = (SELECT AuthorId FROM INSERTED)
FROM Lab15DB_1.dbo.Book
INNER JOIN DELETED ON Lab15DB_1.dbo.Book.AuthorId = DELETED.AuthorId
END
END
GO
There is no problem with case #intRowCount = 1, but I have difficulties with case #intRowCount > 1.
Could you please give me any advice?