Yes, JAL and MU's eastern miles are partners. So in your case, best to use your JAL account.

For others, there are several other options with regards to accruing miles:

1. MU Eastern Miles account - would only suggest this if you live in CN or regularly fly MU
2. Asia Miles (www.asiamiles.com) account - several airline partners, including MU.
3. Delta Sky Miles - MU has a partnership with DL, if you have an account with them, this could be a good option.

For all the above, remember booking class depends on actual miles received.

Personal preference: MU Eastern Miles, but I live in CN and prefer MU for my domestic travel (F & Y)