What kind of vehicle are the "Class B" shares from the prior job held in? Is it an old 401(k) that is just sitting there? If that is the case, then yes, he can either roll it into his new 401(k) (if his new employer accepts rollovers) or into an IRA. Note that if he decides to roll it into an IRA and then convert that IRA to a Roth, he will need to pay income tax on the entire amount converted.
OTOH, if the existing investments are in a regular post-tax brokerage account, he
cannot "roll them over" into his new 401(k) and will need to fund that from his upcoming paychecks. In addition, he also could not roll that over into a new Roth -- he could merely use this year's and last year's contribution thresholds to open a Roth (so
@$14K if he does it by tax day -- $7K for 2018, $7K for 2019). But it would be far better for him to fund a Roth/tIRA with
new savings instead of just tinkering with what kind of bucket his existing savings are in.
In short, don't let the perfect be the enemy of the good. His future financial stability will rest on how much you guys manage to put away over the next 10-20 years -- not on which particular vehicle you put his existing minimal savings into. So max out his IRA and 401(k) to the extent at all possible, put it in a low-cost, broad-market index fund* like VTSAX, and rinse/repeat for the next 15 years or so.
*I am not following why an index fund would be too conservative. You can find an index fund to track just about any kind of market you want, from highly conservative to highly aggressive; there is nothing inherently conservative about an index fund per se. Any kind of low-cost, broad market fund will be fine for his needs.
