In AssetAccountant navigate to Journals and select the journal in question. You will see confirmation that this was posted to your integration partner (Xero in this example).
Underneath the confirmation is a link to view the journal in your integration software. It will prompt you for your login credentials and then navigate to the journal which will include the journal number.
It is in your integration partner that the Journal Number is generated so it won't be reflected in your AssetAccountant journal.
What may be helpful to make the matching process easier is to name your AssetAccountant journals uniquely in the description field so that this is visible in the Journal Description in both systems.
In AssetAccountant I have included #2509-01 in the description being YYMM-JJ (Year,Month, Journal Number.
In my Integration Software it is also identifiable.