Are you sure you want to put the whole xml into attribute of Information1
, like this:
declare @name nvarchar(max), @data xml
select @name = 'mark'
select cast(Information2 as varchar(100)) as n
from table2 as t
where t.Information2.exist('/r/s[@n=sql:variable("@name")]') = 1
for xml raw('s')
update table1 set Information1.modify('insert sql:variable("@data") into (/r)[1]')