number_6

T1 and T3 are actually a single building (T3 was built a decade later than T1 and is much nicer, originally entirely occupied by BA but now BA has cut back most of its MAN service). There is both a walkway and a bus for transfer (the bus also runs to T2, which is a separate terminal and cannot be reached airside except by bus). Walking is the preferred way to go, and takes about 10 minutes if you walk slow (5 min is more typical). So it is a very easy connection. The transfer desk at T3 can issue BP and I presume T1 can do the same, so getting the AA BPs in HEL is desirable but not essential. I've gone through MAN at least a dozen times and it is a very easy transfer. The staff are lightly loaded so they are happy to help if your relatives need it.

One caveat: the AA flight almost always leaves on time (for lots of reasons AA works very hard to accomplish this), and the 2 times that I flew AY in HEL my flights were over 1 hour late. Which might be just enough to miss the connection....but not to worry, if AA MAN-ORD is missed in J, a reroute MAN-LHR-ORD is easily done esp. for a J ticket, as there are dozens of daily flights LHR-USA. Maybe one of the better places to have a tight connection to a once-a-day flight. The BA MAN-JFK flight leaves just before the AA one, so it isn't useful for reroute purposes.