I've just seen this many years later and to me it doesn't make sense and should be simple. Those IDs are just a surrogate key in let's say dbo.transactions.
The system absolutely <HAS> to have a way those amounts and IDs belong to certain clients otherwise how can you determine who made them? The amounts <MUST> belong to different people because sequential IDs can only be for surrogate [internal] use.
Therefore you must be able to join back, and find the client for each amount.
Therefore you join to the table that shows the client, SELECT INTO #WorkTable, and once you have the clients it's a simple SUM(), GROUP BY.
If those IDs are not unique, then they already represent a client and the same thing applies.
My gut feeling is there should always be a GROUP BY possible here? Otherwise you couldn't know which client the amounts belong to?
You have to know what client the amounts belong to - hence you can group them in a temp table.
My £0.2 pence. Peace