Time items can contain hours for up to a week.  When you create an invoice for a month, there might be time, which falls into two months. You can set up the system, so that time items are automatically be split (see Splitting Time+Expense Reports).  This works fine for invoices with weekly, monthly (1st), or bi-monthly (16th) date ranges.

In the Pre-Billing tab, you can enter any date range for the T&E Date from/to.

If the system detects a 'non-standard' date range, a warning is displayed and a "Split Check" link:

It does not mean, that there are actual item crossing the invoice date range boundary, just that there might be.

Each Time item maintains a "First T&E Date" and a "Last T&E Date" in addition to the "T&E Date", which is the start of the week.  When querying the items in Pre-Billing the First/Last dates are used.

When you click on the Splt Check link, a new window is opened to the Time Item Split window copying the parameters of the Pre-Billing Query.

When clicking Query in the Time Item Split window, all items are listed, where the entered hours in an item cross the boundaries in the query.  In the Date range, you would enter the (optional) start and end date of the invoice date range (shown here: Tue-Thu).

When you click Split, the items are split. If there are too many items (in danger of overreaching Salesforce limits), a message will be displayed; just hit Query again and click Split to process the remaining items.

You split all items, if clicking Query returns no records.

Just close the window and go back to the Pre-Billing tab and click Query there; you still will get the warning but may see additional records to invoice.