Modifying a non managed table partition
The best way to do this is:

Let us call your original table Original.


Create two new tables Jan and Feb) matching the schema of Original. You might want to use the partition management tool for this: https://sqlpartitionmgmt.codeplex.com/. Place these new tables directly on the filegroup you want to end up in. Do NOT place them on a partition scheme.
Add a check constraint to Jan limiting the data to only the data in January 2015
Do the same for Feb, but limiting data to February
Script and drop index on Jan and Feb 
Use INSERT Jan WITH (TABLOCK)... SELECT Original WHERE Month = 'January' to populate Jan. This is bulk logged, and hence, should
run at around 40-80MB/sec with minimal impact on the transaction log
As above, for February.
Add indexes back on Jan and Feb
Switch out the old January/February partition from Original to an empty table. Original now has no 2015 records (validate this)
SPLIT the January partition function of Original on the February/January boundary (and any other months you want to prepare for)
ALTER TABLE Jan SWITCH TO Original PARTITION x where x is the partition number of January
ALTER TABLE Feb SWITCH TO Original PARTITION y, where y is the partition number of February
Profit


This is the fastest way to achieve the result with minimal impact on the disk system and transaction log.

It is rather complicated, but learning Partition Fu tricks like these are key to getting the best out of SQL Server partitioning.