The petitioning U.S. entity files Form I-129 and pays the amounts in the current USCIS fee schedule, Form G-1055, with premium processing optional. Corporate structuring, legal advice and relocation are separate and usually larger.
Count the integration work as part of the cost
Hypothetical example: the company budgets filing amounts and immigration counsel and then meets a second set of bills for corporate structuring, cross-border tax advice and payroll set-up in the American company. Build the budget in four parts: government amounts per the current G-1055 schedule; corporate and tax advice on the ownership chain and on how the director will be paid; immigration representation and document preparation; and relocation for the household, including temporary accommodation.
Add the cost of covering the director's Coalhurst duties during the assignment, and the possibility that a first approval period is shorter than the integration project. Where the American operation has been trading for less than a year, expect a one-year initial period and plan the budget across two filings rather than one.