The JSA system examines your joint assets, so transferring the money from one account to another would make no difference.
However you state that you're both aged around 60. Up until April of this year that was the age when both men and women became entitled to to Pension Guarantee Credit. That age is now gradually rising (for both men and women) in line with the gradual increase in the State Pension age for women.
Read the general information here:
http://www.direct.gov...ow_income/dg_10018692
Then click on the link for the State Pension Age Calculator. Enter your own date of birth (and, of course, set your gender to 'Female') to find out when you're entitled to your State Pension (and hence also to Pension Guarantee Credit). Then enter your husband's date of birth but LEAVE THE GENDER SET TO FEMALE. (That's because HIS entitlement to Pension Guarantee Credit is based upon when a WOMAN, born on the same day as him, becomes entitled to the Credit). Hopefully you'll find that one, or both, of you will already be entitled to Pension Guarantee Credit, or will shortly become so.
Chris