Well, from my experiences with portable Mac computers; power adapters, cable
adapters, removable duckhead toggle parts, for iBook 12" G3-500/G4-1.33; Power-
Book 12" aluminum G4-1.5; MacBook1.1 13-inch 2006; & MacBook Pro 2012 13-inch.
Both part numbers you've shown identify correctly per date of manufacture
as official genuine Apple power adapters. [Genuine Replacements from Apple
also exist; but most of those use different inventory numbers.]
These I know well enough, and decidedly without question, about these items.
The Adapter, shown to be broken? That Duckhead, can be further removed.
And the main adapter body, should look like the one without
Duckhead or flip-head section. That "Flip-head" is not repairable.
Those may be purchased separately from OWC or other reseller.
These power adapters, original specification officially sold by Apple
have several replacement part numbers; not all show same numbers.
Here's some examples of correct spec replacements from Apple.
In addition to retail sourced above Power Apple Extension Cable
(*) Apple Genuine 85W MagSafe Power Adapter for MacBook Pro (2006-2012) *NEW*
Mfr P/N: MA357LL/A | OWC SKU: APLMA357LLA [Original $79.00 Only $29.75]
https://eshop.macsales.com/item/Apple/MA357LLA/
(*) Apple Genuine 85W MagSafe Power Adapter for MacBook Pro 13", 15" & 17" Models.
Bulk Flip-Plug include Very Good/New Condition
For all 2006 to 2011, 2012 (Non-Retina) MacBook Pro 13", 15", 17"
Models. Flip Plug Included. Bulk Packaged. 90 Day OWC Warranty.
Mfr P/N: MC556LL/A | OWC SKU: APLMC556LLAB [Was $79.00 - Only $38.75]
https://eshop.macsales.com/item/Apple/MC556LLAB/
(*) Apple Service Part: 1.8 Meter (72") Apple Genuine AC Power Cable - Good/Fair Condition, 'Grade C Used'
Mfr P/N: APLPWRCBLMSAC | OWC SKU: APLPWRCBLMSAC [Only $3.75]
https://eshop.macsales.com/item/Apple/PWRCBLMSAC/
Apple Service Part: Apple Genuine AC Power 'Flip Plug' for Magsafe/Magsafe2
Mfr P/N: 603-2618 | OWC SKU: APLPWRFLIPAC [Only $7.75 New]
https://eshop.macsales.com/item/Apple/PWRFLIPAC/
A fair semi-skilled hands-on person could take broken flip/duckhead part, off.
Take-off MagSafe "flip-plug" & Attach a Cable. ~ Those fit tightly; I've several.
(One adapter from iPad, w/ lower 12W output: I use with my iPhone to charge.)
As many official genuine Apple replacement part numbers for these, yours
are fairly easily replaced by genuine official power cable adapters. OWC is
an authorized Apple reseller and has various replacement/upgrade parts.
(Those 'Apple Extension Cables' fit almost/all Apple adapters made.)