There is no way to adjust what fiscal month/year a transaction is counted towards. Instead, you have to do an RT (Reverse Transaction) on the transaction to bring it down to $0, and then post the transaction again with the correct fiscal month/year on it.

Note:  Be sure to check that the Fiscal month/year on the batch item is the same as the original transaction when adjusting the existing transaction to $0.  You must make sure that the fiscal month/year on the batch item is the same as the original transaction, otherwise you will end up with the original transaction still counting towards the fiscal month/year it is in, and just have a negative amount added to the current fiscal month/year.

For example, if the current Fiscal month/year is 12/6 and you post a $1,500 GF transaction in Fiscal month/year 1/2017, but you decide to change the fiscal year, the following might happen if the adjustment is NOT handled properly:
 
You do an RT to zero it out, but it has a fiscal month/year 1/2016, then you end up $1500 still counting towards 1/2017, but get a -$1500 in 12/2016 (which results in having $1500 less than the total sum for that fiscal month/year than you would expect):
 
ADJUSTMENT_SEQ
FISCAL_YEAR
FISCAL_MONTHPAYMENT_AMOUNTSTS
1201711500I
2201612-1500I
32016120A
 
To avoid this outcome, when you adjust the original transaction that was in 1/2017, make certain that the Batch Summary screen shows the Fiscal month/year 1/2017 as well, so that the negative and positive cancel each other out in the same fiscal month/year.

Properly adjusted, it would look like this:
 
ADJUSTMENT_SEQFISCAL_YEARFISCAL_MONTHPAYMENT_AMOUNTSTS
1201711500I
220171-1500I
3201710A

Which sums up to $0 for 1/2017.

In the event that you already adjusted the Gift down to $0 with a different Fiscal month/year (like in the first example), where the new active transaction is in the wrong Fiscal year, you will then need to follow these steps to correct it:

1. Do another RT adjustment to set the $0 amount back up to the original amount in the same fiscal month/year you did the adjustment in.
So in the first example, you would need to adjust it back from $0 to $1500 in fiscal month/year 1/2016, so that you no longer have a -$1500.  In other words, the -$1500 and newly added $1500 will balance out to $0 so you no longer have an unwanted negative in 1/2016.

2. Do another RT adjustment to set the gift back down to zero, but this time, have it in the fiscal month/year that it was in originally.
So in the first example, you would adjust the now $1500 gift back to $0, but make sure the fiscal month/year is 1/2017, so you will get a -$1500 to cancel out the original $1500.