Uses b43 so it works after installing the b43-open firmware and modprobing b43legacy module. https://www.parabola.nu/packages/libre/x86_64/linux-libre-firmware/

Has the same ID for both the wireless and LAN models.

dmesg

[    7.645601] Support for cores revisions 0x17 and 0x18 disabled by module param allhwsupport=0. Try b43.allhwsupport=1
[    7.645688] b43: probe of bcma0:1 failed with error -524
[    7.645769] Broadcom 43xx driver loaded [ Features: PNLS ]
[    7.742876] brcmsmac bcma0:1: mfg 4bf core 812 rev 24 class 0 irq 17

lspci -vmmnn

Slot:	02:00.0
Class:	Network controller [0280]
Vendor:	Broadcom Corporation [14e4]
Device:	BCM4313 802.11b/g/n Wireless LAN Controller [4727]
SVendor:	Wistron NeWeb Corp. [185f]
SDevice:	Device [051a]
Rev:	01

lspci -nnk

02:00.0 Network controller [0280]: Broadcom Corporation BCM4313 802.11b/g/n Wireless LAN Controller [14e4:4727] (rev 01)
	Subsystem: Wistron NeWeb Corp. Device [185f:051a]
	Kernel driver in use: bcma-pci-bridge
	Kernel modules: bcma, brcmsmac

lspci -vvnnk

06:00.0 Network controller [0280]: Broadcom Limited BCM4313 802.11bgn Wireless Network Adapter [14e4:4727] (rev 01)
	Subsystem: Hewlett-Packard Company BCM4313 802.11bgn Wireless Network Adapter [103c:145c]
	Control: I/O- Mem+ BusMaster+ SpecCycle- MemWINV- VGASnoop- ParErr- Stepping- SERR- FastB2B- DisINTx-
	Status: Cap+ 66MHz- UDF- FastB2B- ParErr- DEVSEL=fast >TAbort- <TAbort- <MAbort- >SERR- <PERR- INTx-
	Latency: 0, Cache Line Size: 64 bytes
	Interrupt: pin A routed to IRQ 17
	NUMA node: 0
	Region 0: Memory at 92100000 (64-bit, non-prefetchable) [size=16K]
	Capabilities: [40] Power Management version 3
		Flags: PMEClk- DSI- D1+ D2+ AuxCurrent=0mA PME(D0-,D1-,D2-,D3hot-,D3cold-)
		Status: D0 NoSoftRst+ PME-Enable- DSel=0 DScale=2 PME-
	Capabilities: [58] Vendor Specific Information: Len=78 <?>
	Capabilities: [48] MSI: Enable- Count=1/1 Maskable- 64bit+
		Address: 0000000000000000  Data: 0000
	Capabilities: [d0] Express (v1) Endpoint, MSI 00
		DevCap:	MaxPayload 128 bytes, PhantFunc 0, Latency L0s <4us, L1 unlimited
			ExtTag+ AttnBtn- AttnInd- PwrInd- RBE+ FLReset- SlotPowerLimit 0.000W
		DevCtl:	Report errors: Correctable- Non-Fatal- Fatal- Unsupported-
			RlxdOrd- ExtTag+ PhantFunc- AuxPwr- NoSnoop-
			MaxPayload 128 bytes, MaxReadReq 128 bytes
		DevSta:	CorrErr+ UncorrErr- FatalErr- UnsuppReq+ AuxPwr+ TransPend-
		LnkCap:	Port #0, Speed 2.5GT/s, Width x1, ASPM L0s L1, Exit Latency L0s <4us, L1 <64us
			ClockPM+ Surprise- LLActRep+ BwNot- ASPMOptComp-
		LnkCtl:	ASPM L0s L1 Enabled; RCB 64 bytes Disabled- CommClk+
			ExtSynch- ClockPM- AutWidDis- BWInt- AutBWInt-
		LnkSta:	Speed 2.5GT/s, Width x1, TrErr- Train- SlotClk+ DLActive+ BWMgmt- ABWMgmt-
	Capabilities: [100 v1] Advanced Error Reporting
		UESta:	DLP- SDES- TLP- FCP- CmpltTO- CmpltAbrt- UnxCmplt- RxOF- MalfTLP- ECRC- UnsupReq- ACSViol-
		UEMsk:	DLP- SDES- TLP- FCP- CmpltTO- CmpltAbrt- UnxCmplt- RxOF- MalfTLP- ECRC- UnsupReq- ACSViol-
		UESvrt:	DLP+ SDES- TLP- FCP+ CmpltTO- CmpltAbrt- UnxCmplt- RxOF+ MalfTLP+ ECRC- UnsupReq- ACSViol-
		CESta:	RxErr- BadTLP- BadDLLP- Rollover- Timeout- NonFatalErr-
		CEMsk:	RxErr- BadTLP- BadDLLP- Rollover- Timeout- NonFatalErr+
		AERCap:	First Error Pointer: 14, GenCap+ CGenEn- ChkCap+ ChkEn-
	Capabilities: [13c v1] Virtual Channel
		Caps:	LPEVC=0 RefClk=100ns PATEntryBits=1
		Arb:	Fixed- WRR32- WRR64- WRR128-
		Ctrl:	ArbSelect=Fixed
		Status:	InProgress-
		VC0:	Caps:	PATOffset=00 MaxTimeSlots=1 RejSnoopTrans-
			Arb:	Fixed- WRR32- WRR64- WRR128- TWRR128- WRR256-
			Ctrl:	Enable+ ID=0 ArbSelect=Fixed TC/VC=ff
			Status:	NegoPending- InProgress-
	Capabilities: [160 v1] Device Serial Number 00-00-19-ff-ff-7b-c4-46
	Capabilities: [16c v1] Power Budgeting <?>
	Kernel driver in use: bcma-pci-bridge
	Kernel modules: bcma