Getting Identity values to use as FK in an INSTEAD OF trigger
Tables:

CREATE TABLE dbo.Claim
(
    DataRowID   bigint IDENTITY NOT NULL,
    ClaimColumn integer NOT NULL,

    CONSTRAINT PK_Claim
        PRIMARY KEY CLUSTERED (DataRowID)
);
GO
CREATE TABLE dbo.ClaimExtended
(
    ClaimDataRowID  bigint NOT NULL,
    ExtendedColumn  integer NOT NULL,

    CONSTRAINT PK_ClaimExtended
        PRIMARY KEY CLUSTERED (ClaimDataRowID),

    CONSTRAINT FK_ClaimExtended_Claim
        FOREIGN KEY (ClaimDataRowID)
        REFERENCES dbo.Claim (DataRowID)
);


View:

CREATE VIEW dbo.MyView
WITH SCHEMABINDING
AS
    SELECT
        c.DataRowID,
        c.ClaimColumn,
        ce.ExtendedColumn
    FROM dbo.Claim AS c
    JOIN dbo.ClaimExtended AS ce ON
        ce.ClaimDataRowID = c.DataRowID;


Instead-of trigger:

CREATE TRIGGER trgMyView_IOI
ON dbo.MyView
INSTEAD OF INSERT
AS
BEGIN
    SET NOCOUNT ON;
    SET ROWCOUNT 0;

    DECLARE @ExtendedRows AS TABLE
    (
        ClaimDataRowID  bigint PRIMARY KEY, 
        ExtendedColumn  integer NOT NULL
    );

    MERGE dbo.Claim AS c
    USING INSERTED AS ins ON 1 = 0
    WHEN NOT MATCHED THEN 
        INSERT (ClaimColumn)
        VALUES (ins.ClaimColumn)
    OUTPUT
        INSERTED.DataRowID,
        ins.ExtendedColumn
    INTO @ExtendedRows 
        (
            ClaimDataRowID,
            ExtendedColumn
        );

    INSERT dbo.ClaimExtended
        (ClaimDataRowID, ExtendedColumn)
    SELECT
        er.ClaimDataRowID,
        er.ExtendedColumn
    FROM @ExtendedRows AS er;
END;


Example usage:

INSERT dbo.MyView
    (ClaimColumn, ExtendedColumn)
VALUES
    (1000, 2000),
    (1001, 2001);
GO
SELECT
    mv.DataRowID,
    mv.ClaimColumn,
    mv.ExtendedColumn
FROM dbo.MyView AS mv;


Output: