TL;DR
If he changes employer now, before him getting the H1B visa stamped (i.e., he is not on H1B status yet.), can his new employer get his H1B transferred to them?
Yes.
It matters not if you already got a visa sticker for your H1b in order for a new employer to apply for a new petition for you under the existing cap allocation.
Longer
The article you provided explains that clearly.
The sentence:
"The individual must be under H-1B status."
is wrong. It should read "The individual must have an approved H-1B petition".
For most people under H1b these would be the same thing, but not in the case you described for your friend. Using the terms "H1b Status" or "H1b visa" for the approved H1b petition is pretty common, but sometimes the semantic differences become confusing - as in this case.
Here's the source (USCIS):
You must meet the following criteria to be classified as an H-1B temporary worker:
- You must have an employer-employee relationship with the petitioning U.S. employer.
- Your job must qualify as a specialty occupation by meeting one of the following criteria:
- A bachelor’s or higher degree or its equivalent is normally the minimum requirement for the particular position;
- The degree requirement is common for the position in the industry, or the job is so complex or unique that it can only be performed by someone with at least a bachelor’s degree in a field related to the position;
- The employer normally requires a degree or its equivalent for the position; or
- The nature of the specific duties is so specialized and complex that the knowledge required to perform the duties is usually associated with the attainment of a bachelor’s or higher degree (For more information, see 8 CFR section 214.2(h)(4)(iii)(A)).
- Your job must be in a specialty occupation related to your field of study;
- The petitioning employer must submit evidence that the U.S. Department of Labor has certified a labor condition application;
- You must be paid at least the actual or prevailing wage for your occupation, whichever is higher; and
- An H-1B visa number must be available at the time of filing the petition, unless the petition is exempt from numerical limits.
Very Long
It appears that there's some confusion on the matter, so after I answered the question, I'll clear up some of the confusion.
Visa vs Status
Visa is a sticker attached to your passport. It is issued by a US Consulate, and is a document shown to the CBP officer at the port of entry to confirm that the consulate has evaluated you and found you qualified to enter the country with a given status (H1b in this case). That's the only use for the visa, it has no other use and serves as evidence to nothing but the fact that at some point the consulate made that determination.
Status is given to you by the CBP officer at the port of entry, or by the USCIS if you're changing status from within the country. The evidence of your status is the form I-94. It may or may not match the status listed on the visa you used to enter. It may or may not be valid for the time beyond the expiration of your visa.
H1B Approval
What's being approved is the employer's petition to hire you as a nonimmigrant employee, which gives you the eligibility for H1b status. The approvals are subject to annual caps (unless cap-exempt employer), and for an approved petition a cap has to be allocated.
Once the petition has been approved you can either ask for an immediate status change (then I-94 with the new status would be attached to the approval notice) or a consular processing (in which case the approval notice will have details of the consulate to which the case was forwarded for visa considerations, and your current status will stay the same if you're already in the country). Once the petition is approved for a certain year, you can change the status to it once you started your employment and all the other conditions are met (including the year start, which for immigration purposes starts on Oct 1st).
If you're already in the US under a different status (F1 in this case), you may remain in that status even if the H1b petition has been approved. But if you didn't change status to H1b within a year from the approval, the approval would be revoked and the quota cap allocation removed. It can, however, be "recaptured" under certain conditions.
There's no requirement for you to be in any specific status (or in the country at all) to transfer your cap allocation from one petition to another (see the above USCIS link).
H1B "Activation"
There's no such thing.
H1b Visa Transfer
No such thing either, despite the many reference to it you may find online.
H1b Status Trasnfer
You'll laugh, but again - no such thing.
So What Is It???
What happens is that the new employer applies for a new H1b approval for you. The petition the new employer submits is not for a transfer or a change - it's a new petition. See details here.
Why do people consider it as "transfer" then?
Because quotas. What happens is that if an H1b quota has been allocated to you, you can use it on as many petitions as you want. The only condition is that you only work for one employer at a time. Thus if you already have an H1b, the new employer doesn't need to get a new cap allocation, you already got one.
This is why transferring from a cap-exempt employer to non-exempt employer is much more difficult than transferring between two employers with the same cap-exemption status.