I am not sure why you are trying to approximate an IIR with an FIR, but an efficient way to do that is with Truncated IIR Filters.
Might be worth exploring.
If you know your 1st or 2nd-order IIR filters and want to truncate their impulse response, this shows you how to do it. Higher order IIRs can be factored into 2nd-order sections, but the finite lengths of the TIIR will add. If you want a higher order IIR with a given truncation length, the thing to do is to parallelize the 2nd-order sections (using partial fraction expansion) and then truncate each parallel 2nd-order section to the same common FIR length.